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y, And (@Membership.mem.{u, u} α (List.{u} α) (@List.instMembership.{u} α) l y) (@Eq.{u + 1} α (f y) x))\n        (@Membership.mem.{u, u} α (List.{u} α) (@List.instMembership.{u} α) l (f 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(List.{u} α) (@List.map.{u, v} α β f) (@List.map.{v, u} β α g)","statement_sha256":"a336088ed377f181c48859858cf60bee8672f53fdfb4b41da058739dd934882c","verification_status":"NOT_CHECKED"},{"authority":"NONE","authorization":"NONE","current_applicability":"NOT_CHECKED","extensions":[],"freshness":"PINNED_HISTORICAL_SOURCE","kind":"theorem","object_contract_version":1,"object_id":"object-1902a2a7fdb7fcf6d83f09acd4b44d2b439c0a15c277260e045167dc651ce02f","qualified_name":"Function.RightInverse.list_map","source":{"commit":"d13f23b723b8a846827a245b89c10fc7d3f11612","module":"Mathlib.Data.List.Basic","path":"Mathlib/Data/List/Basic.lean","range":{"end":{"byte":28066,"column":12,"line":744},"start":{"byte":27908,"column":0,"line":742}},"repository":"https://github.com/leanprover-community/mathlib4","tree":"efa132418a56d0e38c56cc412a06df22178dac5c"},"source_status":"SOURCE_INDEXED","statement":"∀ {α : Type u} {β : Type v} {f : α → β} {g : β → α},\n  @Function.RightInverse.{v + 1, u + 1} β α f g →\n    @Function.RightInverse.{v + 1, u + 1} (List.{v} β) (List.{u} α) (@List.map.{u, v} α β f) (@List.map.{v, u} β α g)","statement_sha256":"c03c0d159296801cd1ed9fd5377b6c8eeec4a23bb325f591da67d26663c98e3d","verification_status":"NOT_CHECKED"},{"authority":"NONE","authorization":"NONE","current_applicability":"NOT_CHECKED","extensions":[],"freshness":"PINNED_HISTORICAL_SOURCE","kind":"theorem","object_contract_version":1,"object_id":"object-66685bf19f20746471d03e2ffbfb04b00f2da64514da25a263b4e6677d04cc29","qualified_name":"Function.Surjective.list_map","source":{"commit":"d13f23b723b8a846827a245b89c10fc7d3f11612","module":"Mathlib.Data.List.Basic","path":"Mathlib/Data/List/Basic.lean","range":{"end":{"byte":29255,"column":60,"line":779},"start":{"byte":29088,"column":0,"line":777}},"repository":"https://github.com/leanprover-community/mathlib4","tree":"efa132418a56d0e38c56cc412a06df22178dac5c"},"source_status":"SOURCE_INDEXED","statement":"∀ {α : Type u} {β : Type v} {f : α → β},\n  @Function.Surjective.{u + 1, v + 1} α β f →\n    @Function.Surjective.{u + 1, v + 1} (List.{u} α) (List.{v} β) (@List.map.{u, v} α β f)","statement_sha256":"44be489d8664e862ad24dd3b11f4cd1c8b51669eae0da451e2e2386bafea84b2","verification_status":"NOT_CHECKED"},{"authority":"NONE","authorization":"NONE","current_applicability":"NOT_CHECKED","extensions":[],"freshness":"PINNED_HISTORICAL_SOURCE","kind":"theorem","object_contract_version":1,"object_id":"object-d2f8d7467bebbe687e05a96e71fa7c9f5d86dd02856c594176a35e55fba62834","qualified_name":"List.Disjoint.map","source":{"commit":"d13f23b723b8a846827a245b89c10fc7d3f11612","module":"Mathlib.Data.List.Basic","path":"Mathlib/Data/List/Basic.lean","range":{"end":{"byte":42824,"column":34,"line":1143},"start":{"byte":42790,"column":0,"line":1143}},"repository":"https://github.com/leanprover-community/mathlib4","tree":"efa132418a56d0e38c56cc412a06df22178dac5c"},"source_status":"SOURCE_INDEXED","statement":"∀ {α : Type u} {β : Type v} {f : α → β} {s t : List.{u} α},\n  @Function.Injective.{u + 1, v + 1} α β f →\n    @List.Disjoint.{u} α s t → @List.Disjoint.{v} β (@List.map.{u, v} α β f s) (@List.map.{u, v} α β f t)","statement_sha256":"fd10ce6764c472d0d17e69640906bfe840c5afa62718c0f316fe054f0f04001f","verification_status":"NOT_CHECKED"},{"authority":"NONE","authorization":"NONE","current_applicability":"NOT_CHECKED","extensions":[],"freshness":"PINNED_HISTORICAL_SOURCE","kind":"theorem","object_contract_version":1,"object_id":"object-c2a01e7e65f20b4f36da883570db67772e4a112c7f1fc4a856b3a40b35543532","qualified_name":"List.Disjoint.map_iff","source":{"commit":"d13f23b723b8a846827a245b89c10fc7d3f11612","module":"Mathlib.Data.List.Basic","path":"Mathlib/Data/List/Basic.lean","range":{"end":{"byte":43191,"column":46,"line":1151},"start":{"byte":43005,"column":0,"line":1149}},"repository":"https://github.com/leanprover-community/mathlib4","tree":"efa132418a56d0e38c56cc412a06df22178dac5c"},"source_status":"SOURCE_INDEXED","statement":"∀ {α : Type u} {β : Type v} {f : α → β} {s t : List.{u} α},\n  @Function.Injective.{u + 1, v + 1} α β f →\n    Iff (@List.Disjoint.{v} β (@List.map.{u, v} α β f s) 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(@List.map.{u, v} α β f t) → @List.Disjoint.{u} α s t","statement_sha256":"515c65ad3f23055055891a5349f7e47cc9daa0d9d56e35f987028b6f51345fed","verification_status":"NOT_CHECKED"},{"authority":"NONE","authorization":"NONE","current_applicability":"NOT_CHECKED","extensions":[],"freshness":"PINNED_HISTORICAL_SOURCE","kind":"theorem","object_contract_version":1,"object_id":"object-54ad00d311d9725345c4d11b6aae88b23d2b40f3d4412a3a5760721b863ff2db","qualified_name":"List.Forall.imp","source":{"commit":"d13f23b723b8a846827a245b89c10fc7d3f11612","module":"Mathlib.Data.List.Basic","path":"Mathlib/Data/List/Basic.lean","range":{"end":{"byte":41466,"column":38,"line":1108},"start":{"byte":41249,"column":0,"line":1103}},"repository":"https://github.com/leanprover-community/mathlib4","tree":"efa132418a56d0e38c56cc412a06df22178dac5c"},"source_status":"SOURCE_INDEXED","statement":"∀ {α : Type u} {p q : α → Prop},\n  (∀ (x : α), p x → q x) → ∀ {l : List.{u} α}, @List.Forall.{u} α p l → @List.Forall.{u} α q l","statement_sha256":"33b30d0b50bdb80ea460ce615ca500c6a0f996260e84d1afd93f03b198d0ac7e","verification_status":"NOT_CHECKED"},{"authority":"NONE","authorization":"NONE","current_applicability":"NOT_CHECKED","extensions":[],"freshness":"PINNED_HISTORICAL_SOURCE","kind":"theorem","object_contract_version":1,"object_id":"object-8156252a34f6a4f2e7f2fb9a74f5617a4fa424c6f858201b28dc8759e15e6486","qualified_name":"List.IsPrefix.idxOf_eq_of_mem","source":{"commit":"d13f23b723b8a846827a245b89c10fc7d3f11612","module":"Mathlib.Data.List.Basic","path":"Mathlib/Data/List/Basic.lean","range":{"end":{"byte":22034,"column":38,"line":587},"start":{"byte":21844,"column":0,"line":584}},"repository":"https://github.com/leanprover-community/mathlib4","tree":"efa132418a56d0e38c56cc412a06df22178dac5c"},"source_status":"SOURCE_INDEXED","statement":"∀ {α : Type u} {l₁ l₂ : List.{u} α} [inst : BEq.{u} α] [@LawfulBEq.{u} α inst],\n  @List.IsPrefix.{u} α l₁ l₂ →\n    ∀ {a : α},\n      @Membership.mem.{u, u} α 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BEq.{u} α] [@LawfulBEq.{u} α inst],\n  @List.IsPrefix.{u} α l₁ l₂ →\n    ∀ (a : α), @LE.le.{0} Nat instLENat (@List.idxOf.{u} α inst a l₁) (@List.idxOf.{u} α inst a 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(@List.idxOf.{u} α inst a l₂)\n        (@HAdd.hAdd.{0, 0, 0} Nat Nat Nat (@instHAdd.{0} Nat instAddNat)\n          (@HSub.hSub.{0, 0, 0} Nat Nat Nat (@instHSub.{0} Nat instSubNat) (@List.length.{u} α l₂)\n            (@List.length.{u} α l₁))\n          (@List.idxOf.{u} α inst a l₁))","statement_sha256":"2c5971e6082ffd94f9aedca7dc28f852cb1bc35f5c07022c07f00feb5ffe856c","verification_status":"NOT_CHECKED"},{"authority":"NONE","authorization":"NONE","current_applicability":"NOT_CHECKED","extensions":[],"freshness":"PINNED_HISTORICAL_SOURCE","kind":"theorem","object_contract_version":1,"object_id":"object-5bd2de005262a45cb837c6fe35d0f89d18e8312315c2c4eaae29fd4aebd14d9b","qualified_name":"List.Perm.disjoint_left","source":{"commit":"d13f23b723b8a846827a245b89c10fc7d3f11612","module":"Mathlib.Data.List.Basic","path":"Mathlib/Data/List/Basic.lean","range":{"end":{"byte":43359,"column":41,"line":1155},"start":{"byte":43193,"column":0,"line":1153}},"repository":"https://github.com/leanprover-community/mathlib4","tree":"efa132418a56d0e38c56cc412a06df22178dac5c"},"source_status":"SOURCE_INDEXED","statement":"∀ {α : Type u} {l₁ l₂ l : List.{u} α},\n  @List.Perm.{u} α l₁ l₂ → Iff (@List.Disjoint.{u} α l₁ l) (@List.Disjoint.{u} α l₂ l)","statement_sha256":"b57ff5c21cad01f5f7c90e97c873331789012818c934a84cb797d1a40423d7ad","verification_status":"NOT_CHECKED"},{"authority":"NONE","authorization":"NONE","current_applicability":"NOT_CHECKED","extensions":[],"freshness":"PINNED_HISTORICAL_SOURCE","kind":"theorem","object_contract_version":1,"object_id":"object-55b9511a0ff91a7fabe58619aa443740f506ffd2fc8bd04e926b4409d2c4ae96","qualified_name":"List.Perm.disjoint_right","source":{"commit":"d13f23b723b8a846827a245b89c10fc7d3f11612","module":"Mathlib.Data.List.Basic","path":"Mathlib/Data/List/Basic.lean","range":{"end":{"byte":43529,"column":42,"line":1159},"start":{"byte":43361,"column":0,"line":1157}},"repository":"https://github.com/leanprover-community/mathlib4","tree":"efa132418a56d0e38c56cc412a06df22178dac5c"},"source_status":"SOURCE_INDEXED","statement":"∀ {α : Type u} {l₁ l₂ l : List.{u} α},\n  @List.Perm.{u} α l₁ l₂ → Iff (@List.Disjoint.{u} α l l₁) (@List.Disjoint.{u} α l l₂)","statement_sha256":"7ee95389bff79499e0f9e3227a79ff6faa16e4ff8af86470cc36d1475828fff5","verification_status":"NOT_CHECKED"},{"authority":"NONE","authorization":"NONE","current_applicability":"NOT_CHECKED","extensions":[],"freshness":"PINNED_HISTORICAL_SOURCE","kind":"theorem","object_contract_version":1,"object_id":"object-800cb01044d2731176ae8d0642dc8cfbf0b93207d603efb6136ce80d7d2c51a8","qualified_name":"List.Sublist.antisymm","source":{"commit":"d13f23b723b8a846827a245b89c10fc7d3f11612","module":"Mathlib.Data.List.Basic","path":"Mathlib/Data/List/Basic.lean","range":{"end":{"byte":20182,"column":37,"line":533},"start":{"byte":20059,"column":0,"line":532}},"repository":"https://github.com/leanprover-community/mathlib4","tree":"efa132418a56d0e38c56cc412a06df22178dac5c"},"source_status":"SOURCE_INDEXED","statement":"∀ {α : Type u} {l₁ l₂ : List.{u} α},\n  @List.Sublist.{u} α l₁ l₂ → @List.Sublist.{u} α l₂ l₁ → @Eq.{u + 1} (List.{u} α) l₁ l₂","statement_sha256":"4450dab505bcb1dafac77348c653f62571b345c12b7e13e4fbcfd8cd80db4575","verification_status":"NOT_CHECKED"},{"authority":"NONE","authorization":"NONE","current_applicability":"NOT_CHECKED","extensions":[],"freshness":"PINNED_HISTORICAL_SOURCE","kind":"theorem","object_contract_version":1,"object_id":"object-dc002387bbfa9aa697ca927ae83bec5a9160b1a584ad9f9f41f0ed0953648765","qualified_name":"List.Sublist.of_cons_of_ne","source":{"commit":"d13f23b723b8a846827a245b89c10fc7d3f11612","module":"Mathlib.Data.List.Basic","path":"Mathlib/Data/List/Basic.lean","range":{"end":{"byte":20564,"column":21,"line":543},"start":{"byte":20315,"column":0,"line":540}},"repository":"https://github.com/leanprover-community/mathlib4","tree":"efa132418a56d0e38c56cc412a06df22178dac5c"},"source_status":"SOURCE_INDEXED","statement":"∀ {α : Type u} {l₁ l₂ : List.{u} α} {a b : α},\n  @Ne.{u + 1} α a b →\n    @List.Sublist.{u} α (@List.cons.{u} α a l₁) (@List.cons.{u} α b l₂) → @List.Sublist.{u} α (@List.cons.{u} α a l₁) l₂","statement_sha256":"42de7966ee6a959e69077d4345e0ad2343294f30696e7933ff60edac228c933a","verification_status":"NOT_CHECKED"},{"authority":"NONE","authorization":"NONE","current_applicability":"NOT_CHECKED","extensions":[],"freshness":"PINNED_HISTORICAL_SOURCE","kind":"theorem","object_contract_version":1,"object_id":"object-c3539d04dd84e09e53e764358494546a08c7da7278ba233b5ae00a8ce35bce99","qualified_name":"List.append_cons_inj_of_notMem","source":{"commit":"d13f23b723b8a846827a245b89c10fc7d3f11612","module":"Mathlib.Data.List.Basic","path":"Mathlib/Data/List/Basic.lean","range":{"end":{"byte":33937,"column":7,"line":884},"start":{"byte":33026,"column":0,"line":871}},"repository":"https://github.com/leanprover-community/mathlib4","tree":"efa132418a56d0e38c56cc412a06df22178dac5c"},"source_status":"SOURCE_INDEXED","statement":"∀ {α : Type u} {x₁ x₂ z₁ z₂ : List.{u} α} {a₁ a₂ : α},\n  a₂ ∉ x₁ →\n    a₂ ∉ z₁ →\n      Iff\n        (@Eq.{u + 1} (List.{u} α)\n          (@HAppend.hAppend.{u, u, u} (List.{u} α) (List.{u} α) (List.{u} α)\n            (@instHAppendOfAppend.{u} (List.{u} α) (@List.instAppend.{u} α)) x₁ (@List.cons.{u} α a₁ z₁))\n          (@HAppend.hAppend.{u, u, u} (List.{u} α) (List.{u} α) (List.{u} α)\n            (@instHAppendOfAppend.{u} (List.{u} α) (@List.instAppend.{u} α)) x₂ (@List.cons.{u} α a₂ z₂)))\n        (And (@Eq.{u + 1} (List.{u} α) x₁ x₂) (And (@Eq.{u + 1} α a₁ a₂) (@Eq.{u + 1} (List.{u} α) z₁ z₂)))","statement_sha256":"764516a3f8a964a79f5d12b7811a3c8a42353b6c312d00fc44e50eb9fdbf9488","verification_status":"NOT_CHECKED"},{"authority":"NONE","authorization":"NONE","current_applicability":"NOT_CHECKED","extensions":[],"freshness":"PINNED_HISTORICAL_SOURCE","kind":"theorem","object_contract_version":1,"object_id":"object-b7a77268cea145c5116cc3edcc4128eafedf733b46e659ea161f84b242b0c13f","qualified_name":"List.append_eq_has_append","source":{"commit":"d13f23b723b8a846827a245b89c10fc7d3f11612","module":"Mathlib.Data.List.Basic","path":"Mathlib/Data/List/Basic.lean","range":{"end":{"byte":7218,"column":5,"line":199},"start":{"byte":7120,"column":0,"line":198}},"repository":"https://github.com/leanprover-community/mathlib4","tree":"efa132418a56d0e38c56cc412a06df22178dac5c"},"source_status":"SOURCE_INDEXED","statement":"∀ {α : Type u} {L₁ L₂ : List.{u} α},\n  @Eq.{u + 1} (List.{u} α) (@List.append.{u} α L₁ L₂)\n    (@HAppend.hAppend.{u, u, u} (List.{u} α) (List.{u} α) (List.{u} α)\n      (@instHAppendOfAppend.{u} (List.{u} α) (@List.instAppend.{u} α)) L₁ L₂)","statement_sha256":"71255351e5aeabda2835bfc5c91c6aba3085e355c71140e20bf112b5e510953f","verification_status":"NOT_CHECKED"},{"authority":"NONE","authorization":"NONE","current_applicability":"NOT_CHECKED","extensions":[],"freshness":"PINNED_HISTORICAL_SOURCE","kind":"theorem","object_contract_version":1,"object_id":"object-614cd7457fba7cc56d40edb75bd644ed2223ebab0a206793a4e11867ff3aa09a","qualified_name":"List.append_left_injective","source":{"commit":"d13f23b723b8a846827a245b89c10fc7d3f11612","module":"Mathlib.Data.List.Basic","path":"Mathlib/Data/List/Basic.lean","range":{"end":{"byte":7440,"column":33,"line":205},"start":{"byte":7331,"column":0,"line":204}},"repository":"https://github.com/leanprover-community/mathlib4","tree":"efa132418a56d0e38c56cc412a06df22178dac5c"},"source_status":"SOURCE_INDEXED","statement":"∀ {α : Type u} (t : List.{u} α),\n  @Function.Injective.{u + 1, u + 1} (List.{u} α) (List.{u} α) fun s =>\n    @HAppend.hAppend.{u, u, u} (List.{u} α) (List.{u} α) (List.{u} α)\n      (@instHAppendOfAppend.{u} (List.{u} α) (@List.instAppend.{u} α)) s t","statement_sha256":"92cbaf599e36590ac31f21e7071909f2f7c541fcfab5576bc8f07084dc054296","verification_status":"NOT_CHECKED"},{"authority":"NONE","authorization":"NONE","current_applicability":"NOT_CHECKED","extensions":[],"freshness":"PINNED_HISTORICAL_SOURCE","kind":"theorem","object_contract_version":1,"object_id":"object-2786302bddf0d4d2dcd7d587cfd349b02139a275878f8d7702882f8d33a3d3cd","qualified_name":"List.append_right_injective","source":{"commit":"d13f23b723b8a846827a245b89c10fc7d3f11612","module":"Mathlib.Data.List.Basic","path":"Mathlib/Data/List/Basic.lean","range":{"end":{"byte":7329,"column":32,"line":202},"start":{"byte":7220,"column":0,"line":201}},"repository":"https://github.com/leanprover-community/mathlib4","tree":"efa132418a56d0e38c56cc412a06df22178dac5c"},"source_status":"SOURCE_INDEXED","statement":"∀ {α : Type u} (s : List.{u} α),\n  @Function.Injective.{u + 1, u + 1} (List.{u} α) (List.{u} α) fun t =>\n    @HAppend.hAppend.{u, u, u} (List.{u} α) (List.{u} α) (List.{u} α)\n      (@instHAppendOfAppend.{u} (List.{u} α) (@List.instAppend.{u} α)) s t","statement_sha256":"cf45ba9e9f413d0fc4a28a9559472e54a7219127d604a2c0d66b15a353cf652a","verification_status":"NOT_CHECKED"},{"authority":"NONE","authorization":"NONE","current_applicability":"NOT_CHECKED","extensions":[],"freshness":"PINNED_HISTORICAL_SOURCE","kind":"theorem","object_contract_version":1,"object_id":"object-080f5bc39b0a4f271e766d1121d8852a4f620997852793bfce27237ed4e4b381","qualified_name":"List.append_subset_of_subset_of_subset","source":{"commit":"d13f23b723b8a846827a245b89c10fc7d3f11612","module":"Mathlib.Data.List.Basic","path":"Mathlib/Data/List/Basic.lean","range":{"end":{"byte":6727,"column":63,"line":186},"start":{"byte":6522,"column":0,"line":184}},"repository":"https://github.com/leanprover-community/mathlib4","tree":"efa132418a56d0e38c56cc412a06df22178dac5c"},"source_status":"SOURCE_INDEXED","statement":"∀ {α : Type u} {l₁ l₂ l : List.{u} α},\n  @HasSubset.Subset.{u} (List.{u} α) (@List.instHasSubset.{u} α) l₁ l →\n    @HasSubset.Subset.{u} (List.{u} α) (@List.instHasSubset.{u} α) l₂ l →\n      @HasSubset.Subset.{u} (List.{u} α) (@List.instHasSubset.{u} α)\n        (@HAppend.hAppend.{u, u, u} (List.{u} α) (List.{u} α) (List.{u} α)\n          (@instHAppendOfAppend.{u} (List.{u} α) (@List.instAppend.{u} α)) l₁ l₂)\n        l","statement_sha256":"01fe03647614dded1fb298ae5321a7ac336079aa662256bb1f711f2776587954","verification_status":"NOT_CHECKED"},{"authority":"NONE","authorization":"NONE","current_applicability":"NOT_CHECKED","extensions":[],"freshness":"PINNED_HISTORICAL_SOURCE","kind":"theorem","object_contract_version":1,"object_id":"object-b2ba8e2a6975a8ad47ef6789df81413a185519768611e56af0f9a357f13b0eb2","qualified_name":"List.bind_eq_flatMap","source":{"commit":"d13f23b723b8a846827a245b89c10fc7d3f11612","module":"Mathlib.Data.List.Basic","path":"Mathlib/Data/List/Basic.lean","range":{"end":{"byte":9632,"column":5,"line":260},"start":{"byte":9525,"column":0,"line":258}},"repository":"https://github.com/leanprover-community/mathlib4","tree":"efa132418a56d0e38c56cc412a06df22178dac5c"},"source_status":"SOURCE_INDEXED","statement":"∀ {α β : Type u_2} (f : α → List.{u_2} β) (l : List.{u_2} α),\n  @Eq.{u_2 + 1} (List.{u_2} β)\n    (@Bind.bind.{u_2, u_2} List.{u_2} (@Monad.toBind.{u_2, u_2} List.{u_2} List.instMonad.{u_2}) α β l f)\n    (@List.flatMap.{u_2, u_2} α β f l)","statement_sha256":"729967574578e30e3644273533679d1dff02a7bc8546b3d42d737ec736ec164f","verification_status":"NOT_CHECKED"},{"authority":"NONE","authorization":"NONE","current_applicability":"NOT_CHECKED","extensions":[],"freshness":"PINNED_HISTORICAL_SOURCE","kind":"theorem","object_contract_version":1,"object_id":"object-cb0e04503a57952f11ac5114f32f835f3188c74574be5920468a10a90c61275b","qualified_name":"List.choose_mem","source":{"commit":"d13f23b723b8a846827a245b89c10fc7d3f11612","module":"Mathlib.Data.List.Basic","path":"Mathlib/Data/List/Basic.lean","range":{"end":{"byte":40454,"column":23,"line":1075},"start":{"byte":40357,"column":0,"line":1074}},"repository":"https://github.com/leanprover-community/mathlib4","tree":"efa132418a56d0e38c56cc412a06df22178dac5c"},"source_status":"SOURCE_INDEXED","statement":"∀ {α : Type u} (p : α → Prop) [inst : @DecidablePred.{u + 1} α p] (l : List.{u} α)\n  (hp : ∃ a, And (@Membership.mem.{u, u} α (List.{u} α) (@List.instMembership.{u} α) l a) (p a)),\n  @Membership.mem.{u, u} α (List.{u} α) (@List.instMembership.{u} α) l (@List.choose.{u} α p inst l hp)","statement_sha256":"0f3a0d4d9205805343f70ecd714ae13da0299ae4722b2c494ab9cd0530e90520","verification_status":"NOT_CHECKED"},{"authority":"NONE","authorization":"NONE","current_applicability":"NOT_CHECKED","extensions":[],"freshness":"PINNED_HISTORICAL_SOURCE","kind":"theorem","object_contract_version":1,"object_id":"object-4f8fed253b65c2c8fa12d25333bad022ebd4f7eac46673ebd0c611fc36f4f2c1","qualified_name":"List.choose_property","source":{"commit":"d13f23b723b8a846827a245b89c10fc7d3f11612","module":"Mathlib.Data.List.Basic","path":"Mathlib/Data/List/Basic.lean","range":{"end":{"byte":40556,"column":23,"line":1078},"start":{"byte":40456,"column":0,"line":1077}},"repository":"https://github.com/leanprover-community/mathlib4","tree":"efa132418a56d0e38c56cc412a06df22178dac5c"},"source_status":"SOURCE_INDEXED","statement":"∀ {α : Type u} (p : α → Prop) [inst : @DecidablePred.{u + 1} α p] (l : List.{u} α)\n  (hp : ∃ a, And (@Membership.mem.{u, u} α (List.{u} α) (@List.instMembership.{u} α) l a) (p a)),\n  p (@List.choose.{u} α p inst l hp)","statement_sha256":"378abba112da79fa37243549be78dd3010010ac89e9e67b57d42bb7cb5d36942","verification_status":"NOT_CHECKED"},{"authority":"NONE","authorization":"NONE","current_applicability":"NOT_CHECKED","extensions":[],"freshness":"PINNED_HISTORICAL_SOURCE","kind":"theorem","object_contract_version":1,"object_id":"object-2376641065cf5c9d6d1ecf2ff756905e843eb04e672f73c449fe8cb674ba5b1f","qualified_name":"List.choose_spec","source":{"commit":"d13f23b723b8a846827a245b89c10fc7d3f11612","module":"Mathlib.Data.List.Basic","path":"Mathlib/Data/List/Basic.lean","range":{"end":{"byte":40355,"column":27,"line":1072},"start":{"byte":40231,"column":0,"line":1071}},"repository":"https://github.com/leanprover-community/mathlib4","tree":"efa132418a56d0e38c56cc412a06df22178dac5c"},"source_status":"SOURCE_INDEXED","statement":"∀ {α : Type u} (p : α → Prop) [inst : @DecidablePred.{u + 1} α p] (l : List.{u} α)\n  (hp : ∃ a, And (@Membership.mem.{u, u} α (List.{u} α) (@List.instMembership.{u} α) l a) (p a)),\n  And (@Membership.mem.{u, u} α (List.{u} α) (@List.instMembership.{u} α) l (@List.choose.{u} α p inst l hp))\n    (p (@List.choose.{u} α p inst l hp))","statement_sha256":"3da1ff7420b502f8e190daef847c806039d7112b8630352e3b6fd7ab8f6f978d","verification_status":"NOT_CHECKED"},{"authority":"NONE","authorization":"NONE","current_applicability":"NOT_CHECKED","extensions":[],"freshness":"PINNED_HISTORICAL_SOURCE","kind":"theorem","object_contract_version":1,"object_id":"object-535d0373269d86088fa9c1c8a0b9e7d3bedd9a1f2ad9878c0257d51f27e10df3","qualified_name":"List.comp_map","source":{"commit":"d13f23b723b8a846827a245b89c10fc7d3f11612","module":"Mathlib.Data.List.Basic","path":"Mathlib/Data/List/Basic.lean","range":{"end":{"byte":27404,"column":14,"line":726},"start":{"byte":27107,"column":0,"line":721}},"repository":"https://github.com/leanprover-community/mathlib4","tree":"efa132418a56d0e38c56cc412a06df22178dac5c"},"source_status":"SOURCE_INDEXED","statement":"∀ {α : Type u} {β : Type v} {γ : Type w} (h : β → γ) (g : α → β) (l : List.{u} α),\n  @Eq.{w + 1} (List.{w} γ) (@List.map.{u, w} α γ (@Function.comp.{u + 1, v + 1, w + 1} α β γ h g) l)\n    (@List.map.{v, w} β γ h (@List.map.{u, v} α β g l))","statement_sha256":"e7113ae22944327854ed3005df5297933d3690447cbee13ed4a6e6f8f6f1dc6d","verification_status":"NOT_CHECKED"},{"authority":"NONE","authorization":"NONE","current_applicability":"NOT_CHECKED","extensions":[],"freshness":"PINNED_HISTORICAL_SOURCE","kind":"theorem","object_contract_version":1,"object_id":"object-20cd61cc94a217962f25a5256e6d0b7dd9d7e8194c6bf2a75f8e5ce681dc5e38","qualified_name":"List.concat_eq_reverse_cons","source":{"commit":"d13f23b723b8a846827a245b89c10fc7d3f11612","module":"Mathlib.Data.List.Basic","path":"Mathlib/Data/List/Basic.lean","range":{"end":{"byte":10394,"column":7,"line":287},"start":{"byte":10287,"column":0,"line":286}},"repository":"https://github.com/leanprover-community/mathlib4","tree":"efa132418a56d0e38c56cc412a06df22178dac5c"},"source_status":"SOURCE_INDEXED","statement":"∀ {α : Type u} (a : α) (l : List.{u} α),\n  @Eq.{u + 1} (List.{u} α) (@List.concat.{u} α l a) (@List.reverse.{u} α (@List.cons.{u} α a (@List.reverse.{u} α l)))","statement_sha256":"10d7184d9a82902e01e48864834a4e44b50e70d67c4316632b99fbe1c08f6205","verification_status":"NOT_CHECKED"},{"authority":"NONE","authorization":"NONE","current_applicability":"NOT_CHECKED","extensions":[],"freshness":"PINNED_HISTORICAL_SOURCE","kind":"theorem","object_contract_version":1,"object_id":"object-e2124cc2698712829126c450d415d058bf0814dac071c385fd7daedb825bf5a5","qualified_name":"List.cons_head!_tail","source":{"commit":"d13f23b723b8a846827a245b89c10fc7d3f11612","module":"Mathlib.Data.List.Basic","path":"Mathlib/Data/List/Basic.lean","range":{"end":{"byte":16668,"column":37,"line":451},"start":{"byte":16536,"column":0,"line":450}},"repository":"https://github.com/leanprover-community/mathlib4","tree":"efa132418a56d0e38c56cc412a06df22178dac5c"},"source_status":"SOURCE_INDEXED","statement":"∀ {α : Type u} [inst : Inhabited.{u + 1} α] {l : List.{u} α},\n  @Ne.{u + 1} (List.{u} α) l (@List.nil.{u} α) →\n    @Eq.{u + 1} (List.{u} α) (@List.cons.{u} α (@List.head!.{u} α inst l) (@List.tail.{u} α l)) l","statement_sha256":"f675ae302dd3e341c9c9d8090e5ab4e7df86f0c835b7a5689b33b97e598f9ece","verification_status":"NOT_CHECKED"},{"authority":"NONE","authorization":"NONE","current_applicability":"NOT_CHECKED","extensions":[],"freshness":"PINNED_HISTORICAL_SOURCE","kind":"theorem","object_contract_version":1,"object_id":"object-fe025d6fc294b1c2cd1b37ca10366e21aed4e77bd4f8ce84d7273a04647acdef","qualified_name":"List.cons_head?_tail","source":{"commit":"d13f23b723b8a846827a245b89c10fc7d3f11612","module":"Mathlib.Data.List.Basic","path":"Mathlib/Data/List/Basic.lean","range":{"end":{"byte":16389,"column":15,"line":444},"start":{"byte":16193,"column":0,"line":440}},"repository":"https://github.com/leanprover-community/mathlib4","tree":"efa132418a56d0e38c56cc412a06df22178dac5c"},"source_status":"SOURCE_INDEXED","statement":"∀ {α : Type u} {l : List.{u} α} {a : α},\n  @Membership.mem.{u, u} α (Option.{u} α) (@Option.instMembership.{u} α) (@List.head?.{u} α l) a →\n    @Eq.{u + 1} (List.{u} α) (@List.cons.{u} α a (@List.tail.{u} α l)) l","statement_sha256":"79699fbf5b363b35d7b2ce354b3b76cec2f089e77b0bc4b30c456a4a24465418","verification_status":"NOT_CHECKED"},{"authority":"NONE","authorization":"NONE","current_applicability":"NOT_CHECKED","extensions":[],"freshness":"PINNED_HISTORICAL_SOURCE","kind":"theorem","object_contract_version":1,"object_id":"object-55b7914b31549a2f7afc988daa2b016a2527088c07c0ce091ad76d5054e51762","qualified_name":"List.cons_injective","source":{"commit":"d13f23b723b8a846827a245b89c10fc7d3f11612","module":"Mathlib.Data.List.Basic","path":"Mathlib/Data/List/Basic.lean","range":{"end":{"byte":1386,"column":93,"line":53},"start":{"byte":1293,"column":0,"line":53}},"repository":"https://github.com/leanprover-community/mathlib4","tree":"efa132418a56d0e38c56cc412a06df22178dac5c"},"source_status":"SOURCE_INDEXED","statement":"∀ {α : Type u} {a : α}, @Function.Injective.{u + 1, u + 1} (List.{u} α) (List.{u} α) (@List.cons.{u} α a)","statement_sha256":"e68eecd4e530c31a86e577c0637de2a45471ad96e57642b821c05b9ab3dbd44e","verification_status":"NOT_CHECKED"},{"authority":"NONE","authorization":"NONE","current_applicability":"NOT_CHECKED","extensions":[],"freshness":"PINNED_HISTORICAL_SOURCE","kind":"theorem","object_contract_version":1,"object_id":"object-4c0b3d3ea648122d673a86ce36e9ad2965ba306dfaa10479cd414a4c1517d601","qualified_name":"List.cons_sublist_cons'","source":{"commit":"d13f23b723b8a846827a245b89c10fc7d3f11612","module":"Mathlib.Data.List.Basic","path":"Mathlib/Data/List/Basic.lean","range":{"end":{"byte":19825,"column":7,"line":525},"start":{"byte":19702,"column":0,"line":524}},"repository":"https://github.com/leanprover-community/mathlib4","tree":"efa132418a56d0e38c56cc412a06df22178dac5c"},"source_status":"SOURCE_INDEXED","statement":"∀ {α : Type u} {l₁ l₂ : List.{u} α} {a b : α},\n  Iff (@List.Sublist.{u} α (@List.cons.{u} α a l₁) (@List.cons.{u} α b l₂))\n    (Or (@List.Sublist.{u} α (@List.cons.{u} α a l₁) l₂) (And (@Eq.{u + 1} α a b) (@List.Sublist.{u} α l₁ l₂)))","statement_sha256":"e37a732d05ca42d8948386579bbe011456149922817917867b0f27baeeeb5499","verification_status":"NOT_CHECKED"},{"authority":"NONE","authorization":"NONE","current_applicability":"NOT_CHECKED","extensions":[],"freshness":"PINNED_HISTORICAL_SOURCE","kind":"theorem","object_contract_version":1,"object_id":"object-b520b8f316f9cfb47525c28d0da9010cb14825105e3d4087adf9f5b72e985773","qualified_name":"List.cons_subset_of_subset_of_mem","source":{"commit":"d13f23b723b8a846827a245b89c10fc7d3f11612","module":"Mathlib.Data.List.Basic","path":"Mathlib/Data/List/Basic.lean","range":{"end":{"byte":6520,"column":33,"line":182},"start":{"byte":6370,"column":0,"line":180}},"repository":"https://github.com/leanprover-community/mathlib4","tree":"efa132418a56d0e38c56cc412a06df22178dac5c"},"source_status":"SOURCE_INDEXED","statement":"∀ {α : Type u} {a : α} {l m : List.{u} α},\n  @Membership.mem.{u, u} α (List.{u} α) (@List.instMembership.{u} α) m a →\n    @HasSubset.Subset.{u} (List.{u} α) (@List.instHasSubset.{u} α) l m →\n      @HasSubset.Subset.{u} (List.{u} α) (@List.instHasSubset.{u} α) (@List.cons.{u} α a l) m","statement_sha256":"54ca08a347f6bacf28cf047f1dde0b33c3ff9027dc025f43480e7d38be484fdb","verification_status":"NOT_CHECKED"},{"authority":"NONE","authorization":"NONE","current_applicability":"NOT_CHECKED","extensions":[],"freshness":"PINNED_HISTORICAL_SOURCE","kind":"theorem","object_contract_version":1,"object_id":"object-d2949c43525ed9e197e1ad4673b640c80f7971bf44a01a7cb7cb8ccf32de89af","qualified_name":"List.disjoint_map","source":{"commit":"d13f23b723b8a846827a245b89c10fc7d3f11612","module":"Mathlib.Data.List.Basic","path":"Mathlib/Data/List/Basic.lean","range":{"end":{"byte":42788,"column":54,"line":1141},"start":{"byte":42437,"column":0,"line":1137}},"repository":"https://github.com/leanprover-community/mathlib4","tree":"efa132418a56d0e38c56cc412a06df22178dac5c"},"source_status":"SOURCE_INDEXED","statement":"∀ {α : Type u} {β : Type v} {f : α → β} {s t : List.{u} α},\n  @Function.Injective.{u + 1, v + 1} α β f →\n    @List.Disjoint.{u} α s t → @List.Disjoint.{v} β (@List.map.{u, v} α β f s) (@List.map.{u, v} α β f t)","statement_sha256":"fd10ce6764c472d0d17e69640906bfe840c5afa62718c0f316fe054f0f04001f","verification_status":"NOT_CHECKED"},{"authority":"NONE","authorization":"NONE","current_applicability":"NOT_CHECKED","extensions":[],"freshness":"PINNED_HISTORICAL_SOURCE","kind":"theorem","object_contract_version":1,"object_id":"object-1bcf086a979a06ff779a71f2172072ae55806c2cee638b6eb2787ab2ea2b7ea7","qualified_name":"List.disjoint_pmap","source":{"commit":"d13f23b723b8a846827a245b89c10fc7d3f11612","module":"Mathlib.Data.List.Basic","path":"Mathlib/Data/List/Basic.lean","range":{"end":{"byte":42435,"column":47,"line":1135},"start":{"byte":41925,"column":0,"line":1126}},"repository":"https://github.com/leanprover-community/mathlib4","tree":"efa132418a56d0e38c56cc412a06df22178dac5c"},"source_status":"SOURCE_INDEXED","statement":"∀ {α : Type u} {β : Type v} {p : α → Prop} {f : (a : α) → p a → β} {s t : List.{u} α}\n  (hs : ∀ (a : α), @Membership.mem.{u, u} α (List.{u} α) (@List.instMembership.{u} α) s a → p a)\n  (ht : ∀ (a : α), @Membership.mem.{u, u} α (List.{u} α) (@List.instMembership.{u} α) t a → p a),\n  (∀ (a a' : α) (ha : p a) (ha' : p a'), @Eq.{v + 1} β (f a ha) (f a' ha') → @Eq.{u + 1} α a a') →\n    @List.Disjoint.{u} α s t → @List.Disjoint.{v} β (@List.pmap.{u, v} α β p f s hs) (@List.pmap.{u, v} α β p f t ht)","statement_sha256":"3f1be477eb7d49cfd712a3d751539237ca4e9bf9b23db378fe7d5efd573e829d","verification_status":"NOT_CHECKED"},{"authority":"NONE","authorization":"NONE","current_applicability":"NOT_CHECKED","extensions":[],"freshness":"PINNED_HISTORICAL_SOURCE","kind":"theorem","object_contract_version":1,"object_id":"object-317f52bde2ca5f2e7a7f5d4f9816f4a6a7017bdb078b30bcd9565054abdf74a2","qualified_name":"List.disjoint_reverse_left","source":{"commit":"d13f23b723b8a846827a245b89c10fc7d3f11612","module":"Mathlib.Data.List.Basic","path":"Mathlib/Data/List/Basic.lean","range":{"end":{"byte":43679,"column":33,"line":1163},"start":{"byte":43531,"column":0,"line":1161}},"repository":"https://github.com/leanprover-community/mathlib4","tree":"efa132418a56d0e38c56cc412a06df22178dac5c"},"source_status":"SOURCE_INDEXED","statement":"∀ {α : Type u} {l₁ l₂ : List.{u} α}, Iff (@List.Disjoint.{u} α (@List.reverse.{u} α l₁) l₂) (@List.Disjoint.{u} α l₁ l₂)","statement_sha256":"d85a794c715660d98fa62ba25b1734a24e649536db9879fd831cbb1d77b97109","verification_status":"NOT_CHECKED"},{"authority":"NONE","authorization":"NONE","current_applicability":"NOT_CHECKED","extensions":[],"freshness":"PINNED_HISTORICAL_SOURCE","kind":"theorem","object_contract_version":1,"object_id":"object-616e25b3079985fad911a7aa84009957d1673d2d81b45a17ca0e35fb9d7eeba6","qualified_name":"List.disjoint_reverse_right","source":{"commit":"d13f23b723b8a846827a245b89c10fc7d3f11612","module":"Mathlib.Data.List.Basic","path":"Mathlib/Data/List/Basic.lean","range":{"end":{"byte":43831,"column":34,"line":1167},"start":{"byte":43681,"column":0,"line":1165}},"repository":"https://github.com/leanprover-community/mathlib4","tree":"efa132418a56d0e38c56cc412a06df22178dac5c"},"source_status":"SOURCE_INDEXED","statement":"∀ {α : Type u} {l₁ l₂ : List.{u} α}, Iff (@List.Disjoint.{u} α l₁ (@List.reverse.{u} α l₂)) (@List.Disjoint.{u} α l₁ l₂)","statement_sha256":"c4e0c511db7c3939aabe5102a959c7abf132f87c3f12bba0ac4912ef72f005ad","verification_status":"NOT_CHECKED"},{"authority":"NONE","authorization":"NONE","current_applicability":"NOT_CHECKED","extensions":[],"freshness":"PINNED_HISTORICAL_SOURCE","kind":"theorem","object_contract_version":1,"object_id":"object-de6194099c6258d4325a146d1952eefc06213c7f19035603498c8b482661a94e","qualified_name":"List.doubleton_eq","source":{"commit":"d13f23b723b8a846827a245b89c10fc7d3f11612","module":"Mathlib.Data.List.Basic","path":"Mathlib/Data/List/Basic.lean","range":{"end":{"byte":5403,"column":35,"line":152},"start":{"byte":5237,"column":0,"line":150}},"repository":"https://github.com/leanprover-community/mathlib4","tree":"efa132418a56d0e38c56cc412a06df22178dac5c"},"source_status":"SOURCE_INDEXED","statement":"∀ {α : Type u} [inst : DecidableEq.{u + 1} α] {x y : α},\n  @Ne.{u + 1} α x y →\n    @Eq.{u + 1} (List.{u} α)\n      (@Insert.insert.{u, u} α (List.{u} α) (@List.instInsertOfDecidableEq_mathlib.{u} α inst) x\n        (@Singleton.singleton.{u, u} α (List.{u} α) (@List.instSingletonList.{u} α) y))\n      (@List.cons.{u} α x (@List.cons.{u} α y (@List.nil.{u} α)))","statement_sha256":"1337435438f1c0387a8d044e13b7526aaa2e722cd43c714f014075fab3ea109a","verification_status":"NOT_CHECKED"},{"authority":"NONE","authorization":"NONE","current_applicability":"NOT_CHECKED","extensions":[],"freshness":"PINNED_HISTORICAL_SOURCE","kind":"theorem","object_contract_version":1,"object_id":"object-0ea832bc60438d78c942eff63115d681c1131157672421b6b4bed346f0c038ad","qualified_name":"List.dropLast_append_getLast","source":{"commit":"d13f23b723b8a846827a245b89c10fc7d3f11612","module":"Mathlib.Data.List.Basic","path":"Mathlib/Data/List/Basic.lean","range":{"end":{"byte":11843,"column":51,"line":326},"start":{"byte":11540,"column":0,"line":320}},"repository":"https://github.com/leanprover-community/mathlib4","tree":"efa132418a56d0e38c56cc412a06df22178dac5c"},"source_status":"SOURCE_INDEXED","statement":"∀ {α : Type u} {l : List.{u} α} (h : @Ne.{u + 1} (List.{u} α) l (@List.nil.{u} α)),\n  @Eq.{u + 1} (List.{u} α)\n    (@HAppend.hAppend.{u, u, u} (List.{u} α) (List.{u} α) (List.{u} α)\n      (@instHAppendOfAppend.{u} (List.{u} α) (@List.instAppend.{u} α)) (@List.dropLast.{u} α l)\n      (@List.cons.{u} α (@List.getLast.{u} α l h) (@List.nil.{u} α)))\n    l","statement_sha256":"073716f25b4a312740ac82ae1b3ddba6b5ed66e9629cd1998a4ec729ed912fb2","verification_status":"NOT_CHECKED"},{"authority":"NONE","authorization":"NONE","current_applicability":"NOT_CHECKED","extensions":[],"freshness":"PINNED_HISTORICAL_SOURCE","kind":"theorem","object_contract_version":1,"object_id":"object-d1d815f10190bf9f975c7256fc24678244313ab2aefe99134cb41993f8489262","qualified_name":"List.dropLast_append_getLast?","source":{"commit":"d13f23b723b8a846827a245b89c10fc7d3f11612","module":"Mathlib.Data.List.Basic","path":"Mathlib/Data/List/Basic.lean","range":{"end":{"byte":13108,"column":71,"line":357},"start":{"byte":12804,"column":0,"line":352}},"repository":"https://github.com/leanprover-community/mathlib4","tree":"efa132418a56d0e38c56cc412a06df22178dac5c"},"source_status":"SOURCE_INDEXED","statement":"∀ {α : Type u} {l : List.{u} α} (a : α),\n  @Membership.mem.{u, u} α (Option.{u} α) (@Option.instMembership.{u} α) (@List.getLast?.{u} α l) a →\n    @Eq.{u + 1} (List.{u} α)\n      (@HAppend.hAppend.{u, u, u} (List.{u} α) (List.{u} α) (List.{u} α)\n        (@instHAppendOfAppend.{u} (List.{u} α) (@List.instAppend.{u} α)) (@List.dropLast.{u} α l)\n        (@List.cons.{u} α a (@List.nil.{u} α)))\n      l","statement_sha256":"6256c99db530a5bc3e11b0c3105671da8ccc68aaf48a1f75339244908c4c50c7","verification_status":"NOT_CHECKED"},{"authority":"NONE","authorization":"NONE","current_applicability":"NOT_CHECKED","extensions":[],"freshness":"PINNED_HISTORICAL_SOURCE","kind":"theorem","object_contract_version":1,"object_id":"object-5626d1ecbe64c30db39d416522a3ed0b6d0f263242c5a8999b6537e0743cbc06","qualified_name":"List.dropLast_eq_nil_iff","source":{"commit":"d13f23b723b8a846827a245b89c10fc7d3f11612","module":"Mathlib.Data.List.Basic","path":"Mathlib/Data/List/Basic.lean","range":{"end":{"byte":19079,"column":45,"line":507},"start":{"byte":18963,"column":0,"line":506}},"repository":"https://github.com/leanprover-community/mathlib4","tree":"efa132418a56d0e38c56cc412a06df22178dac5c"},"source_status":"SOURCE_INDEXED","statement":"∀ {α : Type u} {l : List.{u} α},\n  Iff (@Eq.{u + 1} (List.{u} α) (@List.dropLast.{u} α l) (@List.nil.{u} α))\n    (@LE.le.{0} Nat instLENat (@List.length.{u} α l) (@OfNat.ofNat.{0} Nat (nat_lit 1) (instOfNatNat (nat_lit 1))))","statement_sha256":"c9c2b4445c8562d801a0b1d5ed7c74998712376df58f3d05aafcedfe711da2f9","verification_status":"NOT_CHECKED"},{"authority":"NONE","authorization":"NONE","current_applicability":"NOT_CHECKED","extensions":[],"freshness":"PINNED_HISTORICAL_SOURCE","kind":"theorem","object_contract_version":1,"object_id":"object-695c4a4c4af31ea9310a8c10875647ea863b21a455e11bcf67e78cce67a6d763","qualified_name":"List.eq_cons_of_length_one","source":{"commit":"d13f23b723b8a846827a245b89c10fc7d3f11612","module":"Mathlib.Data.List.Basic","path":"Mathlib/Data/List/Basic.lean","range":{"end":{"byte":26161,"column":43,"line":690},"start":{"byte":26019,"column":0,"line":689}},"repository":"https://github.com/leanprover-community/mathlib4","tree":"efa132418a56d0e38c56cc412a06df22178dac5c"},"source_status":"SOURCE_INDEXED","statement":"∀ {α : Type u} {l : List.{u} α}\n  (h : @Eq.{1} Nat (@List.length.{u} α l) (@OfNat.ofNat.{0} Nat (nat_lit 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α))","statement_sha256":"99b62e5d77c430b1ce8d7c437f8cca4884aa94ce009a79f7ca1ba83356df58ac","verification_status":"NOT_CHECKED"},{"authority":"NONE","authorization":"NONE","current_applicability":"NOT_CHECKED","extensions":[],"freshness":"PINNED_HISTORICAL_SOURCE","kind":"theorem","object_contract_version":1,"object_id":"object-3e060febee302a6f92f878906a85738e7376b3f6cba0b0c87dc6e1abe53e772b","qualified_name":"List.eq_cons_of_mem_head?","source":{"commit":"d13f23b723b8a846827a245b89c10fc7d3f11612","module":"Mathlib.Data.List.Basic","path":"Mathlib/Data/List/Basic.lean","range":{"end":{"byte":15505,"column":19,"line":418},"start":{"byte":15269,"column":0,"line":414}},"repository":"https://github.com/leanprover-community/mathlib4","tree":"efa132418a56d0e38c56cc412a06df22178dac5c"},"source_status":"SOURCE_INDEXED","statement":"∀ {α : Type u} {x : α} {l : List.{u} α},\n  @Membership.mem.{u, u} α (Option.{u} α) (@Option.instMembership.{u} α) (@List.head?.{u} α l) x →\n    @Eq.{u + 1} (List.{u} α) l (@List.cons.{u} α x (@List.tail.{u} α l))","statement_sha256":"7f99c34f9fb31431d75bec689aa901a7776aa7eb95113c0ec6b2d734b216b3c1","verification_status":"NOT_CHECKED"},{"authority":"NONE","authorization":"NONE","current_applicability":"NOT_CHECKED","extensions":[],"freshness":"PINNED_HISTORICAL_SOURCE","kind":"theorem","object_contract_version":1,"object_id":"object-a39ad80cf82847320c98cf503549c51f4c6096a8c1730cd587e1b20d45dc0127","qualified_name":"List.eq_nil_or_concat'","source":{"commit":"d13f23b723b8a846827a245b89c10fc7d3f11612","module":"Mathlib.Data.List.Basic","path":"Mathlib/Data/List/Basic.lean","range":{"end":{"byte":30120,"column":32,"line":801},"start":{"byte":29963,"column":0,"line":799}},"repository":"https://github.com/leanprover-community/mathlib4","tree":"efa132418a56d0e38c56cc412a06df22178dac5c"},"source_status":"SOURCE_INDEXED","statement":"∀ {α : Type u} (l : List.{u} α),\n  Or (@Eq.{u + 1} (List.{u} α) l (@List.nil.{u} α))\n    (∃ L b,\n      @Eq.{u + 1} (List.{u} α) l\n        (@HAppend.hAppend.{u, u, u} (List.{u} α) (List.{u} α) (List.{u} α)\n          (@instHAppendOfAppend.{u} (List.{u} α) (@List.instAppend.{u} α)) L (@List.cons.{u} α b (@List.nil.{u} α))))","statement_sha256":"0a14ea110b54a179e5b7f02e15bc749b64c72ece8def3dd77d72becbafb317a0","verification_status":"NOT_CHECKED"},{"authority":"NONE","authorization":"NONE","current_applicability":"NOT_CHECKED","extensions":[],"freshness":"PINNED_HISTORICAL_SOURCE","kind":"theorem","object_contract_version":1,"object_id":"object-6335112c9eab75f3c08e203c310934a62f34970e2fe4aebda30973e37011ee73","qualified_name":"List.eq_of_head?_eq_of_tail_eq","source":{"commit":"d13f23b723b8a846827a245b89c10fc7d3f11612","module":"Mathlib.Data.List.Basic","path":"Mathlib/Data/List/Basic.lean","range":{"end":{"byte":19330,"column":57,"line":513},"start":{"byte":19081,"column":0,"line":509}},"repository":"https://github.com/leanprover-community/mathlib4","tree":"efa132418a56d0e38c56cc412a06df22178dac5c"},"source_status":"SOURCE_INDEXED","statement":"∀ {α : Type u} {l₁ l₂ : List.{u} α},\n  @Eq.{u + 1} (Option.{u} α) (@List.head?.{u} α l₁) (@List.head?.{u} α l₂) →\n    @Eq.{u + 1} (List.{u} α) 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(List.{v} β) (@List.instMembership.{v} β)\n      (@List.map.{u, v} α β (@Function.const.{v + 1, u + 1} β α b₂) l) b₁ →\n    @Eq.{v + 1} β b₁ b₂","statement_sha256":"b92bc01ca8fad16d5404fa7b9283482525117ca2916be8a367ec39b69dfa66c7","verification_status":"NOT_CHECKED"},{"authority":"NONE","authorization":"NONE","current_applicability":"NOT_CHECKED","extensions":[],"freshness":"PINNED_HISTORICAL_SOURCE","kind":"theorem","object_contract_version":1,"object_id":"object-d6dd7efb6e328f6a9f3b7ca328a6f5c56d4479210ae096ae73cec923b73d2e1f","qualified_name":"List.eq_of_tail_eq_of_dropLast_eq","source":{"commit":"d13f23b723b8a846827a245b89c10fc7d3f11612","module":"Mathlib.Data.List.Basic","path":"Mathlib/Data/List/Basic.lean","range":{"end":{"byte":19643,"column":68,"line":518},"start":{"byte":19332,"column":0,"line":515}},"repository":"https://github.com/leanprover-community/mathlib4","tree":"efa132418a56d0e38c56cc412a06df22178dac5c"},"source_status":"SOURCE_INDEXED","statement":"∀ {α : Type u} {l₁ l₂ : List.{u} α},\n  @LT.lt.{0} Nat instLTNat (@OfNat.ofNat.{0} Nat (nat_lit 1) (instOfNatNat (nat_lit 1))) (@List.length.{u} α l₁) →\n    @Eq.{u + 1} (List.{u} α) (@List.tail.{u} α l₁) (@List.tail.{u} α l₂) →\n      @Eq.{u + 1} (List.{u} α) (@List.dropLast.{u} α l₁) (@List.dropLast.{u} α l₂) → @Eq.{u + 1} (List.{u} α) l₁ l₂","statement_sha256":"5ed5065c6f18bc72215820fb7dc01e6317c9025b2b077e4816b39e78c7ae610a","verification_status":"NOT_CHECKED"},{"authority":"NONE","authorization":"NONE","current_applicability":"NOT_CHECKED","extensions":[],"freshness":"PINNED_HISTORICAL_SOURCE","kind":"theorem","object_contract_version":1,"object_id":"object-8737531d6bb211827a255bdbc5899e2998f8eb69ed0f0f8ada02dbbee40f4e50","qualified_name":"List.eq_replicate_length","source":{"commit":"d13f23b723b8a846827a245b89c10fc7d3f11612","module":"Mathlib.Data.List.Basic","path":"Mathlib/Data/List/Basic.lean","range":{"end":{"byte":7649,"column":61,"line":211},"start":{"byte":7464,"column":0,"line":209}},"repository":"https://github.com/leanprover-community/mathlib4","tree":"efa132418a56d0e38c56cc412a06df22178dac5c"},"source_status":"SOURCE_INDEXED","statement":"∀ {α : Type u} {a : α} {l : List.{u} α},\n  Iff (@Eq.{u + 1} (List.{u} α) l (@List.replicate.{u} α (@List.length.{u} α l) a))\n    (∀ (b : α), @Membership.mem.{u, u} α (List.{u} α) (@List.instMembership.{u} α) l b → @Eq.{u + 1} α b a)","statement_sha256":"6f7ca4e9838334df48d9f301002f4d22c5011f1a89bef308cd3bc068ad0f07aa","verification_status":"NOT_CHECKED"},{"authority":"NONE","authorization":"NONE","current_applicability":"NOT_CHECKED","extensions":[],"freshness":"PINNED_HISTORICAL_SOURCE","kind":"theorem","object_contract_version":1,"object_id":"object-cbbf91043dc91b108fec566645fdbb62a5a48d96da8670b6b6fc046386db7edf","qualified_name":"List.erase_getElem","source":{"commit":"d13f23b723b8a846827a245b89c10fc7d3f11612","module":"Mathlib.Data.List.Basic","path":"Mathlib/Data/List/Basic.lean","range":{"end":{"byte":39704,"column":37,"line":1048},"start":{"byte":39480,"column":0,"line":1044}},"repository":"https://github.com/leanprover-community/mathlib4","tree":"efa132418a56d0e38c56cc412a06df22178dac5c"},"source_status":"SOURCE_INDEXED","statement":"∀ {ι : Type u_1} [inst : BEq.{u_1} ι] [@LawfulBEq.{u_1} ι inst] {l : List.{u_1} ι} {i : Nat}\n  (hi : @LT.lt.{0} Nat instLTNat i (@List.length.{u_1} ι l)),\n  @List.Perm.{u_1} ι\n    (@List.erase.{u_1} ι inst l\n      (@GetElem.getElem.{u_1, 0, u_1} (List.{u_1} ι) Nat ι\n        (fun as i => @LT.lt.{0} Nat instLTNat i (@List.length.{u_1} ι as)) (@List.instGetElemNatLtLength.{u_1} ι) l i\n        hi))\n    (@List.eraseIdx.{u_1} ι l i)","statement_sha256":"54461e134e3d92f2998be1047b13cbde5564ee9b61fb26d5ad2f247a0c2737cc","verification_status":"NOT_CHECKED"},{"authority":"NONE","authorization":"NONE","current_applicability":"NOT_CHECKED","extensions":[],"freshness":"PINNED_HISTORICAL_SOURCE","kind":"theorem","object_contract_version":1,"object_id":"object-633c2af5ec376dd18d0c7b1b7d3e81fca1fac93072daeb0ff8d65f21a269e1b1","qualified_name":"List.exists_mem_cons_iff","source":{"commit":"d13f23b723b8a846827a245b89c10fc7d3f11612","module":"Mathlib.Data.List.Basic","path":"Mathlib/Data/List/Basic.lean","range":{"end":{"byte":6218,"column":68,"line":170},"start":{"byte":6079,"column":0,"line":169}},"repository":"https://github.com/leanprover-community/mathlib4","tree":"efa132418a56d0e38c56cc412a06df22178dac5c"},"source_status":"SOURCE_INDEXED","statement":"∀ {α : Type u} (p : α → Prop) (a : α) (l : List.{u} α),\n  Iff (∃ x, And (@Membership.mem.{u, u} α (List.{u} α) (@List.instMembership.{u} α) (@List.cons.{u} α a l) x) (p x))\n    (Or (p a) (∃ x, And (@Membership.mem.{u, u} α (List.{u} α) (@List.instMembership.{u} α) l x) (p x)))","statement_sha256":"f180a7cb0c8f3fbb6e65021ef410d1243dbb5b568b5f3e69692572e5053f2811","verification_status":"NOT_CHECKED"},{"authority":"NONE","authorization":"NONE","current_applicability":"NOT_CHECKED","extensions":[],"freshness":"PINNED_HISTORICAL_SOURCE","kind":"theorem","object_contract_version":1,"object_id":"object-aed5c114dd4818f7e468e9320ad8f6340d940f6a0023409cbb67d9e8af1c202d","qualified_name":"List.exists_mem_cons_of","source":{"commit":"d13f23b723b8a846827a245b89c10fc7d3f11612","module":"Mathlib.Data.List.Basic","path":"Mathlib/Data/List/Basic.lean","range":{"end":{"byte":5738,"column":27,"line":160},"start":{"byte":5606,"column":0,"line":159}},"repository":"https://github.com/leanprover-community/mathlib4","tree":"efa132418a56d0e38c56cc412a06df22178dac5c"},"source_status":"SOURCE_INDEXED","statement":"∀ {α : Type u} {p : α → Prop} {a : α} (l : List.{u} α),\n  p a → ∃ x, And (@Membership.mem.{u, u} α (List.{u} α) (@List.instMembership.{u} α) (@List.cons.{u} α a l) x) (p x)","statement_sha256":"f6c5e23f5073a46295f97ae07804c20002ff82e0c62623be419fe74263a2afe9","verification_status":"NOT_CHECKED"},{"authority":"NONE","authorization":"NONE","current_applicability":"NOT_CHECKED","extensions":[],"freshness":"PINNED_HISTORICAL_SOURCE","kind":"theorem","object_contract_version":1,"object_id":"object-d33f4fa4f2f21cdf5df58dd31d89930a54d4c7e9b8744b1a4f47ab6c7aff1f5f","qualified_name":"List.exists_mem_cons_of_exists","source":{"commit":"d13f23b723b8a846827a245b89c10fc7d3f11612","module":"Mathlib.Data.List.Basic","path":"Mathlib/Data/List/Basic.lean","range":{"end":{"byte":5927,"column":58,"line":164},"start":{"byte":5740,"column":0,"line":162}},"repository":"https://github.com/leanprover-community/mathlib4","tree":"efa132418a56d0e38c56cc412a06df22178dac5c"},"source_status":"SOURCE_INDEXED","statement":"∀ {α : Type u} {p : α → Prop} {a : α} {l : List.{u} α},\n  (∃ x, And (@Membership.mem.{u, u} α (List.{u} α) (@List.instMembership.{u} α) l x) (p x)) →\n    ∃ x, And (@Membership.mem.{u, u} α (List.{u} α) (@List.instMembership.{u} α) (@List.cons.{u} α a l) x) (p x)","statement_sha256":"192f6207cab307a2828935137cc3b908eda0772e88d103298af0e8fb3491f697","verification_status":"NOT_CHECKED"},{"authority":"NONE","authorization":"NONE","current_applicability":"NOT_CHECKED","extensions":[],"freshness":"PINNED_HISTORICAL_SOURCE","kind":"theorem","object_contract_version":1,"object_id":"object-61de2ea60fe10b4e668f6089c245304d1a0a00e7abc12eeaa7e8013db2231eae","qualified_name":"List.exists_mem_iff_get","source":{"commit":"d13f23b723b8a846827a245b89c10fc7d3f11612","module":"Mathlib.Data.List.Basic","path":"Mathlib/Data/List/Basic.lean","range":{"end":{"byte":17509,"column":119,"line":468},"start":{"byte":17263,"column":0,"line":466}},"repository":"https://github.com/leanprover-community/mathlib4","tree":"efa132418a56d0e38c56cc412a06df22178dac5c"},"source_status":"SOURCE_INDEXED","statement":"∀ {α : Type u} {l : List.{u} α} {p : α → Prop},\n  Iff (∃ x, And (@Membership.mem.{u, u} α (List.{u} α) (@List.instMembership.{u} α) l x) (p x))\n    (∃ i, p (@List.get.{u} α l i))","statement_sha256":"0559182f2a60141894c0c54ef309d01d5a2a84fa902f34f54ed058be727ecf5e","verification_status":"NOT_CHECKED"},{"authority":"NONE","authorization":"NONE","current_applicability":"NOT_CHECKED","extensions":[],"freshness":"PINNED_HISTORICAL_SOURCE","kind":"theorem","object_contract_version":1,"object_id":"object-a20dca3baf0fe3c0e7c8c5fafc3e040604011700786e770402df8437e6d54915","qualified_name":"List.exists_mem_iff_getElem","source":{"commit":"d13f23b723b8a846827a245b89c10fc7d3f11612","module":"Mathlib.Data.List.Basic","path":"Mathlib/Data/List/Basic.lean","range":{"end":{"byte":17261,"column":133,"line":464},"start":{"byte":16959,"column":0,"line":461}},"repository":"https://github.com/leanprover-community/mathlib4","tree":"efa132418a56d0e38c56cc412a06df22178dac5c"},"source_status":"SOURCE_INDEXED","statement":"∀ {α : Type u} {l : List.{u} α} {p : α → Prop},\n  Iff (∃ x, And (@Membership.mem.{u, u} α (List.{u} α) (@List.instMembership.{u} α) l x) (p x))\n    (∃ i,\n      ∃ (x : @LT.lt.{0} Nat instLTNat i (@List.length.{u} α l)),\n        p\n          (@GetElem.getElem.{u, 0, u} (List.{u} α) Nat α\n            (fun as i => @LT.lt.{0} Nat instLTNat i (@List.length.{u} α as)) (@List.instGetElemNatLtLength.{u} α) l i\n            x))","statement_sha256":"aa2c69c35419113439b8d2e34ba183e6e601fb7b7ee76dd9c31fdff80cefbc91","verification_status":"NOT_CHECKED"},{"authority":"NONE","authorization":"NONE","current_applicability":"NOT_CHECKED","extensions":[],"freshness":"PINNED_HISTORICAL_SOURCE","kind":"theorem","object_contract_version":1,"object_id":"object-d552b1b90f8111cedeef0a2ec78f8822533f999bdbea6a1db54221e0e999762f","qualified_name":"List.exists_of_length_succ","source":{"commit":"d13f23b723b8a846827a245b89c10fc7d3f11612","module":"Mathlib.Data.List.Basic","path":"Mathlib/Data/List/Basic.lean","range":{"end":{"byte":3134,"column":32,"line":95},"start":{"byte":2963,"column":0,"line":93}},"repository":"https://github.com/leanprover-community/mathlib4","tree":"efa132418a56d0e38c56cc412a06df22178dac5c"},"source_status":"SOURCE_INDEXED","statement":"∀ {α : Type u} {n : Nat} (l : List.{u} α),\n  @Eq.{1} Nat (@List.length.{u} α l)\n      (@HAdd.hAdd.{0, 0, 0} Nat Nat Nat (@instHAdd.{0} Nat instAddNat) n\n        (@OfNat.ofNat.{0} Nat (nat_lit 1) (instOfNatNat (nat_lit 1)))) →\n    ∃ h t, @Eq.{u + 1} (List.{u} α) l (@List.cons.{u} α h t)","statement_sha256":"cf2c0ca4e2d58a7183df35e6e035121f19d42bcd859183d5f35cc69e6e77c6b1","verification_status":"NOT_CHECKED"},{"authority":"NONE","authorization":"NONE","current_applicability":"NOT_CHECKED","extensions":[],"freshness":"PINNED_HISTORICAL_SOURCE","kind":"theorem","object_contract_version":1,"object_id":"object-d4f171bdf914db91f9312539c8eb7b9fed5106b4e78d890da8eba760b00a7292","qualified_name":"List.ext_getElem!","source":{"commit":"d13f23b723b8a846827a245b89c10fc7d3f11612","module":"Mathlib.Data.List.Basic","path":"Mathlib/Data/List/Basic.lean","range":{"end":{"byte":25232,"column":79,"line":667},"start":{"byte":24901,"column":0,"line":663}},"repository":"https://github.com/leanprover-community/mathlib4","tree":"efa132418a56d0e38c56cc412a06df22178dac5c"},"source_status":"SOURCE_INDEXED","statement":"∀ {α : Type u} {l₁ l₂ : List.{u} α} [inst : Inhabited.{u + 1} α],\n  @Eq.{1} Nat (@List.length.{u} α l₁) (@List.length.{u} α l₂) →\n    (∀ (n : Nat),\n        @Eq.{u + 1} α\n          (@GetElem?.getElem!.{u, 0, u} (List.{u} α) Nat α\n            (fun as i => @LT.lt.{0} Nat instLTNat i (@List.length.{u} α as)) (@List.instGetElem?NatLtLength.{u} α) inst\n            l₁ n)\n          (@GetElem?.getElem!.{u, 0, u} (List.{u} α) Nat α\n            (fun as i => @LT.lt.{0} Nat instLTNat i (@List.length.{u} α as)) (@List.instGetElem?NatLtLength.{u} α) inst\n            l₂ n)) →\n      @Eq.{u + 1} (List.{u} α) l₁ l₂","statement_sha256":"60b4d59d7d3f9a287cb5396e6412c7ed507f4a4f16232c051a678facb1cbb1c5","verification_status":"NOT_CHECKED"},{"authority":"NONE","authorization":"NONE","current_applicability":"NOT_CHECKED","extensions":[],"freshness":"PINNED_HISTORICAL_SOURCE","kind":"theorem","object_contract_version":1,"object_id":"object-b4d937cf94ae480afbcb7aafdb8a25185a71f7e2e934e0251b2a75073ade815e","qualified_name":"List.ext_getElem?'","source":{"commit":"d13f23b723b8a846827a245b89c10fc7d3f11612","module":"Mathlib.Data.List.Basic","path":"Mathlib/Data/List/Basic.lean","range":{"end":{"byte":24431,"column":7,"line":649},"start":{"byte":24271,"column":0,"line":646}},"repository":"https://github.com/leanprover-community/mathlib4","tree":"efa132418a56d0e38c56cc412a06df22178dac5c"},"source_status":"SOURCE_INDEXED","statement":"∀ {α : Type u} {l₁ l₂ : List.{u} α},\n  (∀ (n : Nat),\n      @LT.lt.{0} Nat instLTNat n (@Max.max.{0} Nat Nat.instMax (@List.length.{u} α l₁) (@List.length.{u} α l₂)) →\n        @Eq.{u + 1} (Option.{u} α)\n          (@GetElem?.getElem?.{u, 0, u} (List.{u} α) Nat α\n            (fun as i => @LT.lt.{0} Nat instLTNat i (@List.length.{u} α as)) (@List.instGetElem?NatLtLength.{u} α) l₁ n)\n          (@GetElem?.getElem?.{u, 0, u} (List.{u} α) Nat α\n            (fun as i => @LT.lt.{0} Nat instLTNat i (@List.length.{u} α as)) (@List.instGetElem?NatLtLength.{u} α) l₂\n            n)) →\n    @Eq.{u + 1} (List.{u} α) l₁ l₂","statement_sha256":"e96526d75efbf631c9751cfdec4dd09d925b3f160038a7d3d002d843643ff965","verification_status":"NOT_CHECKED"},{"authority":"NONE","authorization":"NONE","current_applicability":"NOT_CHECKED","extensions":[],"freshness":"PINNED_HISTORICAL_SOURCE","kind":"theorem","object_contract_version":1,"object_id":"object-7a583e4c7f420e5d2eda197dabeeb0c20acdcf32fd363cea7465a105e97c6c9a","qualified_name":"List.ext_getElem?_iff'","source":{"commit":"d13f23b723b8a846827a245b89c10fc7d3f11612","module":"Mathlib.Data.List.Basic","path":"Mathlib/Data/List/Basic.lean","range":{"end":{"byte":24899,"column":45,"line":661},"start":{"byte":24724,"column":0,"line":659}},"repository":"https://github.com/leanprover-community/mathlib4","tree":"efa132418a56d0e38c56cc412a06df22178dac5c"},"source_status":"SOURCE_INDEXED","statement":"∀ {α : Type u} {l₁ l₂ : List.{u} α},\n  Iff (@Eq.{u + 1} (List.{u} α) l₁ l₂)\n    (∀ (n : Nat),\n      @LT.lt.{0} Nat instLTNat n (@Max.max.{0} Nat Nat.instMax (@List.length.{u} α l₁) (@List.length.{u} α l₂)) →\n        @Eq.{u + 1} (Option.{u} α)\n          (@GetElem?.getElem?.{u, 0, u} (List.{u} α) Nat α\n            (fun as i => @LT.lt.{0} Nat instLTNat i (@List.length.{u} α as)) (@List.instGetElem?NatLtLength.{u} α) l₁ n)\n          (@GetElem?.getElem?.{u, 0, u} (List.{u} α) Nat α\n            (fun as i => @LT.lt.{0} Nat instLTNat i (@List.length.{u} α as)) (@List.instGetElem?NatLtLength.{u} α) l₂\n            n))","statement_sha256":"82cfc34b31574be101ecd87ede292a725c5da6079934bab1c34f26cb431467a5","verification_status":"NOT_CHECKED"},{"authority":"NONE","authorization":"NONE","current_applicability":"NOT_CHECKED","extensions":[],"freshness":"PINNED_HISTORICAL_SOURCE","kind":"theorem","object_contract_version":1,"object_id":"object-fded3af90cd09bdbb3e05debd4d3440b5ac4e066db9fe9fd42c40dd078bd2c84","qualified_name":"List.ext_get_iff","source":{"commit":"d13f23b723b8a846827a245b89c10fc7d3f11612","module":"Mathlib.Data.List.Basic","path":"Mathlib/Data/List/Basic.lean","range":{"end":{"byte":24722,"column":27,"line":657},"start":{"byte":24433,"column":0,"line":651}},"repository":"https://github.com/leanprover-community/mathlib4","tree":"efa132418a56d0e38c56cc412a06df22178dac5c"},"source_status":"SOURCE_INDEXED","statement":"∀ {α : Type u} {l₁ l₂ : List.{u} α},\n  Iff (@Eq.{u + 1} (List.{u} α) l₁ l₂)\n    (And (@Eq.{1} Nat (@List.length.{u} α l₁) (@List.length.{u} α l₂))\n      (∀ (n : Nat) (h₁ : @LT.lt.{0} Nat instLTNat n (@List.length.{u} α l₁))\n        (h₂ : @LT.lt.{0} Nat instLTNat n (@List.length.{u} α l₂)),\n        @Eq.{u + 1} α (@List.get.{u} α l₁ (@Fin.mk (@List.length.{u} α l₁) n h₁))\n          (@List.get.{u} α l₂ (@Fin.mk (@List.length.{u} α l₂) n h₂))))","statement_sha256":"04e4b74ab5678a7e0ee2cec9107d55119ce1fbf53207bc46fb20c2d16bdf38ba","verification_status":"NOT_CHECKED"},{"authority":"NONE","authorization":"NONE","current_applicability":"NOT_CHECKED","extensions":[],"freshness":"PINNED_HISTORICAL_SOURCE","kind":"theorem","object_contract_version":1,"object_id":"object-8e0502e3b3b33445c20806b37930c3b1b7978ac917c8a990af210449f60c3600","qualified_name":"List.filterMap_congr","source":{"commit":"d13f23b723b8a846827a245b89c10fc7d3f11612","module":"Mathlib.Data.List.Basic","path":"Mathlib/Data/List/Basic.lean","range":{"end":{"byte":35369,"column":43,"line":925},"start":{"byte":35183,"column":0,"line":922}},"repository":"https://github.com/leanprover-community/mathlib4","tree":"efa132418a56d0e38c56cc412a06df22178dac5c"},"source_status":"SOURCE_INDEXED","statement":"∀ {α : Type u} {β : Type v} {f g : α → Option.{v} β} {l : List.{u} α},\n  (∀ (x : α),\n      @Membership.mem.{u, u} α (List.{u} α) (@List.instMembership.{u} α) l x → @Eq.{v + 1} (Option.{v} β) (f x) (g x)) →\n    @Eq.{v + 1} (List.{v} β) (@List.filterMap.{u, v} α β f l) (@List.filterMap.{u, v} α β g l)","statement_sha256":"46ae00c5484e195f4f77c3b6213fa4e13622c3ec7d3f5e5e6e4d63e33ecbb545","verification_status":"NOT_CHECKED"},{"authority":"NONE","authorization":"NONE","current_applicability":"NOT_CHECKED","extensions":[],"freshness":"PINNED_HISTORICAL_SOURCE","kind":"theorem","object_contract_version":1,"object_id":"object-c0a3225160863019726798e2dc3eda4c661af3b22277d5381ee8132a7d0eb25a","qualified_name":"List.filterMap_eq_flatMap_toList","source":{"commit":"d13f23b723b8a846827a245b89c10fc7d3f11612","module":"Mathlib.Data.List.Basic","path":"Mathlib/Data/List/Basic.lean","range":{"end":{"byte":35181,"column":26,"line":920},"start":{"byte":34944,"column":0,"line":917}},"repository":"https://github.com/leanprover-community/mathlib4","tree":"efa132418a56d0e38c56cc412a06df22178dac5c"},"source_status":"SOURCE_INDEXED","statement":"∀ {α : Type u} {β : Type v} (f : α → Option.{v} β) (l : List.{u} α),\n  @Eq.{v + 1} (List.{v} β) (@List.filterMap.{u, v} α β f l)\n    (@List.flatMap.{u, v} α β (fun a => @Option.toList.{v} β (f a)) 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x)))","statement_sha256":"2f69e63a49f59f4434a38644cbccbbf7bce3372c69b94c6ac6577a71c8c638f4","verification_status":"NOT_CHECKED"},{"authority":"NONE","authorization":"NONE","current_applicability":"NOT_CHECKED","extensions":[],"freshness":"PINNED_HISTORICAL_SOURCE","kind":"theorem","object_contract_version":1,"object_id":"object-22ac64512d6a77b2fac740062bc5a421d10e12517ca92b2946883baa6a0d0154","qualified_name":"List.filterMap_none","source":{"commit":"d13f23b723b8a846827a245b89c10fc7d3f11612","module":"Mathlib.Data.List.Basic","path":"Mathlib/Data/List/Basic.lean","range":{"end":{"byte":35966,"column":26,"line":941},"start":{"byte":35840,"column":0,"line":938}},"repository":"https://github.com/leanprover-community/mathlib4","tree":"efa132418a56d0e38c56cc412a06df22178dac5c"},"source_status":"SOURCE_INDEXED","statement":"∀ {α : Type u} {β : Type v} (l : List.{u} α),\n  @Eq.{v + 1} (List.{v} β) (@List.filterMap.{u, v} α β (fun x => @Option.none.{v} β) l) (@List.nil.{v} 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l)))","statement_sha256":"15fba55d4b61ea7924044e432a023dda733a59fdb69ca893193fd0fa90b85473","verification_status":"NOT_CHECKED"},{"authority":"NONE","authorization":"NONE","current_applicability":"NOT_CHECKED","extensions":[],"freshness":"PINNED_HISTORICAL_SOURCE","kind":"theorem","object_contract_version":1,"object_id":"object-1d6bef4815e35874e0e12d1667c92d8a635dd0249f811aa232fa3ce5371a04b7","qualified_name":"List.filter_attach'","source":{"commit":"d13f23b723b8a846827a245b89c10fc7d3f11612","module":"Mathlib.Data.List.Basic","path":"Mathlib/Data/List/Basic.lean","range":{"end":{"byte":37589,"column":53,"line":990},"start":{"byte":37255,"column":0,"line":985}},"repository":"https://github.com/leanprover-community/mathlib4","tree":"efa132418a56d0e38c56cc412a06df22178dac5c"},"source_status":"SOURCE_INDEXED","statement":"∀ {α : Type u} (l : List.{u} α)\n  (p : (@Subtype.{u + 1} α fun a => @Membership.mem.{u, u} α (List.{u} α) (@List.instMembership.{u} α) l a) → Bool)\n  [inst : 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l)))","statement_sha256":"ba0df346eb4ad6bbc881bda9382072bc9c8a7cd76b067cd92ea9c6ff5f2eb198","verification_status":"NOT_CHECKED"},{"authority":"NONE","authorization":"NONE","current_applicability":"NOT_CHECKED","extensions":[],"freshness":"PINNED_HISTORICAL_SOURCE","kind":"theorem","object_contract_version":1,"object_id":"object-72a0f1df3d9963df53003226a1cac637b448cf805745776f7560bf0a20dfd04e","qualified_name":"List.filter_comm","source":{"commit":"d13f23b723b8a846827a245b89c10fc7d3f11612","module":"Mathlib.Data.List.Basic","path":"Mathlib/Data/List/Basic.lean","range":{"end":{"byte":38083,"column":22,"line":1000},"start":{"byte":37971,"column":0,"line":999}},"repository":"https://github.com/leanprover-community/mathlib4","tree":"efa132418a56d0e38c56cc412a06df22178dac5c"},"source_status":"SOURCE_INDEXED","statement":"∀ {α : Type u} (p q : α → Bool) (l : List.{u} α),\n  @Eq.{u + 1} (List.{u} α) (@List.filter.{u} α p (@List.filter.{u} α q l))\n    (@List.filter.{u} α q (@List.filter.{u} α 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(@cond.{u + 1} (List.{u} α) (p a) (@List.cons.{u} α a (@List.nil.{u} α)) (@List.nil.{u} α))","statement_sha256":"dae32af0904a230e4e379cb4008bf67d136aee2bd934012739671886f941def7","verification_status":"NOT_CHECKED"},{"authority":"NONE","authorization":"NONE","current_applicability":"NOT_CHECKED","extensions":[],"freshness":"PINNED_HISTORICAL_SOURCE","kind":"theorem","object_contract_version":1,"object_id":"object-6815a05709771ef5570c000c14aea0ef9f7e6932a4f407c1788a94dbeab8503d","qualified_name":"List.filter_subset'","source":{"commit":"d13f23b723b8a846827a245b89c10fc7d3f11612","module":"Mathlib.Data.List.Basic","path":"Mathlib/Data/List/Basic.lean","range":{"end":{"byte":36529,"column":80,"line":964},"start":{"byte":36449,"column":0,"line":964}},"repository":"https://github.com/leanprover-community/mathlib4","tree":"efa132418a56d0e38c56cc412a06df22178dac5c"},"source_status":"SOURCE_INDEXED","statement":"∀ {α : Type u} {p : α → Bool} (l : List.{u} α),\n  @HasSubset.Subset.{u} (List.{u} 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@Eq.{u + 1} α\n        (@GetElem.getElem.{u, 0, u} (List.{u} α) Nat α (fun as i => @LT.lt.{0} Nat instLTNat i (@List.length.{u} α as))\n          (@List.instGetElemNatLtLength.{u} α) (@List.set.{u} α l i a) j hj)\n        (@GetElem.getElem.{u, 0, u} (List.{u} α) Nat α (fun as i => @LT.lt.{0} Nat instLTNat i (@List.length.{u} α as))\n          (@List.instGetElemNatLtLength.{u} α) l j 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(@List.getLast?.{u} α\n        (@HAppend.hAppend.{u, u, u} (List.{u} α) (List.{u} α) (List.{u} α)\n          (@instHAppendOfAppend.{u} (List.{u} α) (@List.instAppend.{u} α)) l₁ l₂))\n      (@List.getLast?.{u} α 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(a : α),\n  @Eq.{u + 1} α\n    (@List.getLast.{u} α\n      (@List.replicate.{u} α\n        (@HAdd.hAdd.{0, 0, 0} Nat Nat Nat (@instHAdd.{0} Nat instAddNat) m\n          (@OfNat.ofNat.{0} Nat (nat_lit 1) (instOfNatNat (nat_lit 1))))\n        a)\n      ⋯)\n    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⋯))","statement_sha256":"d48ffe318069fa7b6aaca11d9807f0fd47942cc283cc9ed2b28de80ec19b8c73","verification_status":"NOT_CHECKED"},{"authority":"NONE","authorization":"NONE","current_applicability":"NOT_CHECKED","extensions":[],"freshness":"PINNED_HISTORICAL_SOURCE","kind":"theorem","object_contract_version":1,"object_id":"object-da752964750e6bf10bb96e23fd7f030b83cedaada128c8cd8baa7ec6abbaa892","qualified_name":"List.get_eq_getElem?","source":{"commit":"d13f23b723b8a846827a245b89c10fc7d3f11612","module":"Mathlib.Data.List.Basic","path":"Mathlib/Data/List/Basic.lean","range":{"end":{"byte":16957,"column":6,"line":459},"start":{"byte":16852,"column":0,"line":457}},"repository":"https://github.com/leanprover-community/mathlib4","tree":"efa132418a56d0e38c56cc412a06df22178dac5c"},"source_status":"SOURCE_INDEXED","statement":"∀ {α : Type u} (l : List.{u} α) (i : Fin (@List.length.{u} α l)),\n  @Eq.{u + 1} α (@List.get.{u} α l i)\n    (@Option.get.{u} α\n      (@GetElem?.getElem?.{u, 0, u} 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(@HAppend.hAppend.{u, u, u} (List.{u} α) (List.{u} α) (List.{u} α)\n          (@instHAppendOfAppend.{u} (List.{u} α) (@List.instAppend.{u} α)) l₁ l₂))\n      (@HAdd.hAdd.{0, 0, 0} Nat Nat Nat (@instHAdd.{0} Nat instAddNat) (@List.length.{u} α l₁)\n        (@List.idxOf.{u} α inst a 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(@List.instInsertOfDecidableEq_mathlib.{u} α inst) (@List.instSingletonList.{u} α)","statement_sha256":"4cdf626628dd2f143619b2b6bb3a5b88404511915531920ccfc9523d938ee080","verification_status":"NOT_CHECKED"},{"authority":"NONE","authorization":"NONE","current_applicability":"NOT_CHECKED","extensions":[],"freshness":"PINNED_HISTORICAL_SOURCE","kind":"definition","object_contract_version":1,"object_id":"object-1bafb5207eb582dafd5b270a663c5219668ba21b5ff4106cecb2cdbb12fe7ece","qualified_name":"List.instSingletonList","source":{"commit":"d13f23b723b8a846827a245b89c10fc7d3f11612","module":"Mathlib.Data.List.Basic","path":"Mathlib/Data/List/Basic.lean","range":{"end":{"byte":4665,"column":73,"line":132},"start":{"byte":4592,"column":0,"line":132}},"repository":"https://github.com/leanprover-community/mathlib4","tree":"efa132418a56d0e38c56cc412a06df22178dac5c"},"source_status":"SOURCE_INDEXED","statement":"{α : Type u} → Singleton.{u, u} α (List.{u} 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(@OfNat.ofNat.{0} Nat (nat_lit 2) (instOfNatNat (nat_lit 2))))\n    (∃ a b, @Eq.{u + 1} (List.{u} α) l (@List.cons.{u} α a (@List.cons.{u} α b (@List.nil.{u} α))))","statement_sha256":"72b53549640f4e02d0b0b149b7d26120918222b7ddd91733785ffa60cb0325a6","verification_status":"NOT_CHECKED"},{"authority":"NONE","authorization":"NONE","current_applicability":"NOT_CHECKED","extensions":[],"freshness":"PINNED_HISTORICAL_SOURCE","kind":"theorem","object_contract_version":1,"object_id":"object-370dfbf5f77d91bdcdc84ab2a62c8cdcac224e3eaa16818662d482634d2e39da","qualified_name":"List.length_eq_two'","source":{"commit":"d13f23b723b8a846827a245b89c10fc7d3f11612","module":"Mathlib.Data.List.Basic","path":"Mathlib/Data/List/Basic.lean","range":{"end":{"byte":4179,"column":27,"line":122},"start":{"byte":4047,"column":0,"line":121}},"repository":"https://github.com/leanprover-community/mathlib4","tree":"efa132418a56d0e38c56cc412a06df22178dac5c"},"source_status":"SOURCE_INDEXED","statement":"∀ {α : Type u} {l : List.{u} α} (h : @Ne.{u + 1} (List.{u} α) l (@List.nil.{u} α)),\n  Iff (@Eq.{1} Nat (@List.length.{u} α l) (@OfNat.ofNat.{0} Nat (nat_lit 2) (instOfNatNat (nat_lit 2))))\n    (@Eq.{u + 1} (List.{u} α) l\n      (@List.cons.{u} α (@List.head.{u} α l h) (@List.cons.{u} α (@List.getLast.{u} α l h) (@List.nil.{u} α))))","statement_sha256":"232690b6d0d528b592c6fda661b5541e313260bd0cad3d155fd7a166975be452","verification_status":"NOT_CHECKED"},{"authority":"NONE","authorization":"NONE","current_applicability":"NOT_CHECKED","extensions":[],"freshness":"PINNED_HISTORICAL_SOURCE","kind":"theorem","object_contract_version":1,"object_id":"object-fa73223d1b75a05f98e812e049518403a94afacbeea40ff4739000720da5f407","qualified_name":"List.length_eraseIdx_add_one","source":{"commit":"d13f23b723b8a846827a245b89c10fc7d3f11612","module":"Mathlib.Data.List.Basic","path":"Mathlib/Data/List/Basic.lean","range":{"end":{"byte":39835,"column":52,"line":1051},"start":{"byte":39706,"column":0,"line":1050}},"repository":"https://github.com/leanprover-community/mathlib4","tree":"efa132418a56d0e38c56cc412a06df22178dac5c"},"source_status":"SOURCE_INDEXED","statement":"∀ {ι : Type u_1} {l : List.{u_1} ι} {i : Nat},\n  @LT.lt.{0} Nat instLTNat i (@List.length.{u_1} ι l) →\n    @Eq.{1} Nat\n      (@HAdd.hAdd.{0, 0, 0} Nat Nat 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@Eq.{1} Nat\n      (@HAdd.hAdd.{0, 0, 0} Nat Nat Nat (@instHAdd.{0} Nat instAddNat) (@List.length.{u} α (@List.erase.{u} α inst l a))\n        (@OfNat.ofNat.{0} Nat (nat_lit 1) (instOfNatNat (nat_lit 1))))\n      (@List.length.{u} α l)","statement_sha256":"35ac356105155aadcd542af81fce1e3900b2ba39a10b4d74327f3a7f91ee49c7","verification_status":"NOT_CHECKED"},{"authority":"NONE","authorization":"NONE","current_applicability":"NOT_CHECKED","extensions":[],"freshness":"PINNED_HISTORICAL_SOURCE","kind":"theorem","object_contract_version":1,"object_id":"object-aec97b72d57d1045ae8189b69bf1d4c57dd87bb3b41ce2dff81c557546ed1f4f","qualified_name":"List.length_injective","source":{"commit":"d13f23b723b8a846827a245b89c10fc7d3f11612","module":"Mathlib.Data.List.Basic","path":"Mathlib/Data/List/Basic.lean","range":{"end":{"byte":3884,"column":40,"line":116},"start":{"byte":3693,"column":0,"line":114}},"repository":"https://github.com/leanprover-community/mathlib4","tree":"efa132418a56d0e38c56cc412a06df22178dac5c"},"source_status":"SOURCE_INDEXED","statement":"∀ {α : Type u} [Subsingleton.{u + 1} α], @Function.Injective.{u + 1, 1} (List.{u} α) Nat (@List.length.{u} 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α)","statement_sha256":"cf477b24ededee0a0666115f6017b2cc4c583744cd8777b08d6b458688ab2fbf","verification_status":"NOT_CHECKED"},{"authority":"NONE","authorization":"NONE","current_applicability":"NOT_CHECKED","extensions":[],"freshness":"PINNED_HISTORICAL_SOURCE","kind":"theorem","object_contract_version":1,"object_id":"object-f5abdd915e0f48a6c431e6ce75b29178ad82554b759b7610920944867d8c0acc","qualified_name":"List.length_pos_iff_ne_nil","source":{"commit":"d13f23b723b8a846827a245b89c10fc7d3f11612","module":"Mathlib.Data.List.Basic","path":"Mathlib/Data/List/Basic.lean","range":{"end":{"byte":2961,"column":50,"line":91},"start":{"byte":2836,"column":0,"line":90}},"repository":"https://github.com/leanprover-community/mathlib4","tree":"efa132418a56d0e38c56cc412a06df22178dac5c"},"source_status":"SOURCE_INDEXED","statement":"∀ {α : Type u} {l : List.{u} α},\n  Iff (@LT.lt.{0} Nat instLTNat (@OfNat.ofNat.{0} Nat (nat_lit 0) (instOfNatNat (nat_lit 0))) (@List.length.{u} α l))\n    (@Ne.{u + 1} 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{α : Type u} {β : Type v} [inst : BEq.{u} α] [@LawfulBEq.{u} α inst] [inst_2 : BEq.{v} β] [@LawfulBEq.{v} β inst_2]\n  {f : α → β},\n  @Function.Injective.{u + 1, v + 1} α β f →\n    ∀ {l₁ l₂ : List.{u} α},\n      @Eq.{v + 1} (List.{v} β) (@List.map.{u, v} α β f (@List.diff.{u} α inst l₁ l₂))\n        (@List.diff.{v} β inst_2 (@List.map.{u, v} α β f l₁) (@List.map.{u, v} α β f 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u_2} α β f l)","statement_sha256":"a591b26915a7722825e90c32736e340b922354950f7dcc5ad91eb4f97050c27e","verification_status":"NOT_CHECKED"},{"authority":"NONE","authorization":"NONE","current_applicability":"NOT_CHECKED","extensions":[],"freshness":"PINNED_HISTORICAL_SOURCE","kind":"theorem","object_contract_version":1,"object_id":"object-61fddab35341ff011f8073d743be1db5929d7f071f7806456a1b1c46c27a604c","qualified_name":"List.map_erase","source":{"commit":"d13f23b723b8a846827a245b89c10fc7d3f11612","module":"Mathlib.Data.List.Basic","path":"Mathlib/Data/List/Basic.lean","range":{"end":{"byte":39182,"column":62,"line":1038},"start":{"byte":38897,"column":0,"line":1035}},"repository":"https://github.com/leanprover-community/mathlib4","tree":"efa132418a56d0e38c56cc412a06df22178dac5c"},"source_status":"SOURCE_INDEXED","statement":"∀ {α : Type u} {β : Type v} [inst : BEq.{u} α] [@LawfulBEq.{u} α inst] [inst_2 : BEq.{v} β] [@LawfulBEq.{v} β inst_2]\n  {f : α → β},\n  @Function.Injective.{u + 1, v + 1} α β f →\n    ∀ {a : α} (l : List.{u} α),\n      @Eq.{v + 1} (List.{v} β) (@List.map.{u, v} α β f (@List.erase.{u} α inst l a))\n        (@List.erase.{v} β inst_2 (@List.map.{u, v} α β f l) (f a))","statement_sha256":"ac4bc7cc4984958508e24174407362051d6f167143dae0a7346c7836ca2d08e6","verification_status":"NOT_CHECKED"},{"authority":"NONE","authorization":"NONE","current_applicability":"NOT_CHECKED","extensions":[],"freshness":"PINNED_HISTORICAL_SOURCE","kind":"theorem","object_contract_version":1,"object_id":"object-a83d26062aef5833cbdffad9301e0e5f4a6250e45941c941f857ff230f37b486","qualified_name":"List.map_filter","source":{"commit":"d13f23b723b8a846827a245b89c10fc7d3f11612","module":"Mathlib.Data.List.Basic","path":"Mathlib/Data/List/Basic.lean","range":{"end":{"byte":37253,"column":40,"line":983},"start":{"byte":37013,"column":0,"line":980}},"repository":"https://github.com/leanprover-community/mathlib4","tree":"efa132418a56d0e38c56cc412a06df22178dac5c"},"source_status":"SOURCE_INDEXED","statement":"∀ {α : Type u} {β : Type v} (p : α → Bool) {f : α → β},\n  @Function.Injective.{u + 1, v + 1} α β f →\n    ∀ (l : List.{u} α)\n      [inst : @DecidablePred.{v + 1} β fun b => 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l))","statement_sha256":"4589bce1dbdcda0da74fc8272d6c7828c8616dafb514c27aaf6551defa222304","verification_status":"NOT_CHECKED"},{"authority":"NONE","authorization":"NONE","current_applicability":"NOT_CHECKED","extensions":[],"freshness":"PINNED_HISTORICAL_SOURCE","kind":"theorem","object_contract_version":1,"object_id":"object-8bd7e76c116049b76ec46bb4d4351b343ab5ba42c189934f2d84a6078b6bc83e","qualified_name":"List.map_foldl_erase","source":{"commit":"d13f23b723b8a846827a245b89c10fc7d3f11612","module":"Mathlib.Data.List.Basic","path":"Mathlib/Data/List/Basic.lean","range":{"end":{"byte":39478,"column":87,"line":1042},"start":{"byte":39184,"column":0,"line":1040}},"repository":"https://github.com/leanprover-community/mathlib4","tree":"efa132418a56d0e38c56cc412a06df22178dac5c"},"source_status":"SOURCE_INDEXED","statement":"∀ {α : Type u} {β : Type v} [inst : BEq.{u} α] [@LawfulBEq.{u} α inst] [inst_2 : BEq.{v} β] [@LawfulBEq.{v} β inst_2]\n  {f : α → β},\n  @Function.Injective.{u + 1, v + 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l₂)","statement_sha256":"84d6085ea1cb4b6be0e09094b69f9d88b0f31127270b8c1a2f369ed881d4d633","verification_status":"NOT_CHECKED"},{"authority":"NONE","authorization":"NONE","current_applicability":"NOT_CHECKED","extensions":[],"freshness":"PINNED_HISTORICAL_SOURCE","kind":"theorem","object_contract_version":1,"object_id":"object-b4f475dacbc7d83c8c0056dfa381168333dcbe42c83e1485cf303af8b74c2cda","qualified_name":"List.map_injective_iff","source":{"commit":"d13f23b723b8a846827a245b89c10fc7d3f11612","module":"Mathlib.Data.List.Basic","path":"Mathlib/Data/List/Basic.lean","range":{"end":{"byte":29086,"column":12,"line":775},"start":{"byte":28881,"column":0,"line":770}},"repository":"https://github.com/leanprover-community/mathlib4","tree":"efa132418a56d0e38c56cc412a06df22178dac5c"},"source_status":"SOURCE_INDEXED","statement":"∀ {α : Type u} {β : Type v} {f : α → β},\n  Iff (@Function.Injective.{u + 1, v + 1} (List.{u} α) (List.{v} β) (@List.map.{u, v} α β f))\n    (@Function.Injective.{u + 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f)","statement_sha256":"82b897a58b705b6d9fe92fba581c1b77b45e2e32157b300eb4ba0ef6691c53c2","verification_status":"NOT_CHECKED"},{"authority":"NONE","authorization":"NONE","current_applicability":"NOT_CHECKED","extensions":[],"freshness":"PINNED_HISTORICAL_SOURCE","kind":"theorem","object_contract_version":1,"object_id":"object-b5e1ce28e3c6d8dd9ccdc621a465f002642d5d030991c1e7fa1b4a36740ce92b","qualified_name":"List.map_leftInverse_iff","source":{"commit":"d13f23b723b8a846827a245b89c10fc7d3f11612","module":"Mathlib.Data.List.Basic","path":"Mathlib/Data/List/Basic.lean","range":{"end":{"byte":28394,"column":52,"line":753},"start":{"byte":28217,"column":0,"line":750}},"repository":"https://github.com/leanprover-community/mathlib4","tree":"efa132418a56d0e38c56cc412a06df22178dac5c"},"source_status":"SOURCE_INDEXED","statement":"∀ {α : Type u} {β : Type v} {f : α → β} {g : β → α},\n  Iff (@Function.LeftInverse.{v + 1, u + 1} (List.{v} β) (List.{u} α) (@List.map.{u, v} α β f) (@List.map.{v, u} β α g))\n    (@Function.LeftInverse.{v + 1, u + 1} β α f g)","statement_sha256":"9742e1a60a487e795937f04de03817620c0faa1827e4923c41e05f1bcbc73436","verification_status":"NOT_CHECKED"},{"authority":"NONE","authorization":"NONE","current_applicability":"NOT_CHECKED","extensions":[],"freshness":"PINNED_HISTORICAL_SOURCE","kind":"theorem","object_contract_version":1,"object_id":"object-32605eb1d8907a3190d20804970bf22d62f9e5c669873776b825fee35686f674","qualified_name":"List.map_reverseAux","source":{"commit":"d13f23b723b8a846827a245b89c10fc7d3f11612","module":"Mathlib.Data.List.Basic","path":"Mathlib/Data/List/Basic.lean","range":{"end":{"byte":10589,"column":52,"line":291},"start":{"byte":10396,"column":0,"line":289}},"repository":"https://github.com/leanprover-community/mathlib4","tree":"efa132418a56d0e38c56cc412a06df22178dac5c"},"source_status":"SOURCE_INDEXED","statement":"∀ {α : Type u} {β : Type v} (f : α → β) (l₁ l₂ : List.{u} α),\n  @Eq.{v + 1} (List.{v} β) (@List.map.{u, v} α β f (@List.reverseAux.{u} α l₁ l₂))\n    (@List.reverseAux.{v} β (@List.map.{u, v} α β f l₁) (@List.map.{u, v} α β f l₂))","statement_sha256":"6aa392894578736d7b129081674fc61451818c1dd98599d1bfc9050739b8ea0b","verification_status":"NOT_CHECKED"},{"authority":"NONE","authorization":"NONE","current_applicability":"NOT_CHECKED","extensions":[],"freshness":"PINNED_HISTORICAL_SOURCE","kind":"theorem","object_contract_version":1,"object_id":"object-8886150af5a5a80fca4b6d3a1156fa4f48c8b239a94aaf65c9eb3be04bbb28e1","qualified_name":"List.map_rightInverse_iff","source":{"commit":"d13f23b723b8a846827a245b89c10fc7d3f11612","module":"Mathlib.Data.List.Basic","path":"Mathlib/Data/List/Basic.lean","range":{"end":{"byte":28543,"column":76,"line":757},"start":{"byte":28396,"column":0,"line":755}},"repository":"https://github.com/leanprover-community/mathlib4","tree":"efa132418a56d0e38c56cc412a06df22178dac5c"},"source_status":"SOURCE_INDEXED","statement":"∀ {α : Type u} {β : Type v} {f : α → β} {g : β → α},\n  Iff\n    (@Function.RightInverse.{v + 1, u + 1} (List.{v} β) (List.{u} α) (@List.map.{u, v} α β f) (@List.map.{v, u} β α g))\n    (@Function.RightInverse.{v + 1, u + 1} β α f g)","statement_sha256":"d98d5f9dad279c4ac517f09230b308547ce047cec93de181932f2a59b5d10b17","verification_status":"NOT_CHECKED"},{"authority":"NONE","authorization":"NONE","current_applicability":"NOT_CHECKED","extensions":[],"freshness":"PINNED_HISTORICAL_SOURCE","kind":"theorem","object_contract_version":1,"object_id":"object-c56946ae1d52eaa1c7cdbf48fac8872c64e79fbc13d6e63fc4b50b8b6738faf9","qualified_name":"List.map_subset_iff","source":{"commit":"d13f23b723b8a846827a245b89c10fc7d3f11612","module":"Mathlib.Data.List.Basic","path":"Mathlib/Data/List/Basic.lean","range":{"end":{"byte":7005,"column":25,"line":192},"start":{"byte":6729,"column":0,"line":188}},"repository":"https://github.com/leanprover-community/mathlib4","tree":"efa132418a56d0e38c56cc412a06df22178dac5c"},"source_status":"SOURCE_INDEXED","statement":"∀ {α : Type u} {β : Type v} {l₁ l₂ : List.{u} α} (f : α → β),\n  @Function.Injective.{u + 1, v + 1} α β f →\n    Iff\n      (@HasSubset.Subset.{v} (List.{v} β) (@List.instHasSubset.{v} β) (@List.map.{u, v} α β f l₁)\n        (@List.map.{u, v} α β f l₂))\n      (@HasSubset.Subset.{u} (List.{u} α) (@List.instHasSubset.{u} α) l₁ l₂)","statement_sha256":"d3e2d53222f817b749450fb82db5fd0495c49576f913218eaea5e96065d3a2a8","verification_status":"NOT_CHECKED"},{"authority":"NONE","authorization":"NONE","current_applicability":"NOT_CHECKED","extensions":[],"freshness":"PINNED_HISTORICAL_SOURCE","kind":"theorem","object_contract_version":1,"object_id":"object-e080ea0e890ae51dd42848b57a5e18908b5245b2e70bec76486f4f615ad765e8","qualified_name":"List.map_surjective_iff","source":{"commit":"d13f23b723b8a846827a245b89c10fc7d3f11612","module":"Mathlib.Data.List.Basic","path":"Mathlib/Data/List/Basic.lean","range":{"end":{"byte":29471,"column":45,"line":785},"start":{"byte":29257,"column":0,"line":781}},"repository":"https://github.com/leanprover-community/mathlib4","tree":"efa132418a56d0e38c56cc412a06df22178dac5c"},"source_status":"SOURCE_INDEXED","statement":"∀ {α : Type u} {β : Type v} {f : α → β},\n  Iff (@Function.Surjective.{u + 1, v + 1} (List.{u} α) (List.{v} β) (@List.map.{u, v} α β f))\n    (@Function.Surjective.{u + 1, v + 1} α β f)","statement_sha256":"d6fd2ea5f733fa3a9a972da37a0130f4fa061224bd06191bfb446f0b6ef16a12","verification_status":"NOT_CHECKED"},{"authority":"NONE","authorization":"NONE","current_applicability":"NOT_CHECKED","extensions":[],"freshness":"PINNED_HISTORICAL_SOURCE","kind":"theorem","object_contract_version":1,"object_id":"object-ec82d38222eefa4503fc0aa685bb25d82edf9b5567d2a7bcd0ce6f95ccd7f653","qualified_name":"List.mem_dropLast_iff_idxOf_lt","source":{"commit":"d13f23b723b8a846827a245b89c10fc7d3f11612","module":"Mathlib.Data.List.Basic","path":"Mathlib/Data/List/Basic.lean","range":{"end":{"byte":23033,"column":49,"line":613},"start":{"byte":22854,"column":0,"line":611}},"repository":"https://github.com/leanprover-community/mathlib4","tree":"efa132418a56d0e38c56cc412a06df22178dac5c"},"source_status":"SOURCE_INDEXED","statement":"∀ {α : Type u} [inst : BEq.{u} α] [@LawfulBEq.{u} α inst] {l : List.{u} α} {a : α},\n  @Membership.mem.{u, u} α (List.{u} α) 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1)))))","statement_sha256":"c38848db6b28fa3c9e84653508ddd422bc244bf1057874c390fe3f25fe03f5c4","verification_status":"NOT_CHECKED"},{"authority":"NONE","authorization":"NONE","current_applicability":"NOT_CHECKED","extensions":[],"freshness":"PINNED_HISTORICAL_SOURCE","kind":"theorem","object_contract_version":1,"object_id":"object-4eda4675ef0dd83436208ae948db6e6143034b47836bd142990e484ddaf5bdde","qualified_name":"List.mem_dropLast_of_mem_of_ne_getLast","source":{"commit":"d13f23b723b8a846827a245b89c10fc7d3f11612","module":"Mathlib.Data.List.Basic","path":"Mathlib/Data/List/Basic.lean","range":{"end":{"byte":14240,"column":33,"line":383},"start":{"byte":14069,"column":0,"line":381}},"repository":"https://github.com/leanprover-community/mathlib4","tree":"efa132418a56d0e38c56cc412a06df22178dac5c"},"source_status":"SOURCE_INDEXED","statement":"∀ {α : Type u} {l : List.{u} α} {a : α} (ha : @Membership.mem.{u, u} α (List.{u} α) (@List.instMembership.{u} α) l a),\n  @Ne.{u + 1} α a (@List.getLast.{u} α l ⋯) →\n    @Membership.mem.{u, u} α (List.{u} α) (@List.instMembership.{u} α) (@List.dropLast.{u} α l) a","statement_sha256":"55b789bcdfa75d221e972591827ff0849e0988aa7d01233acb7947efd19732f4","verification_status":"NOT_CHECKED"},{"authority":"NONE","authorization":"NONE","current_applicability":"NOT_CHECKED","extensions":[],"freshness":"PINNED_HISTORICAL_SOURCE","kind":"theorem","object_contract_version":1,"object_id":"object-1fe9f310cf7c34ee1fb048e30e71793a43d9d2861be55e5f1e4a709a2ef84b2d","qualified_name":"List.mem_dropLast_of_mem_of_ne_getLast?","source":{"commit":"d13f23b723b8a846827a245b89c10fc7d3f11612","module":"Mathlib.Data.List.Basic","path":"Mathlib/Data/List/Basic.lean","range":{"end":{"byte":14584,"column":50,"line":391},"start":{"byte":14416,"column":0,"line":389}},"repository":"https://github.com/leanprover-community/mathlib4","tree":"efa132418a56d0e38c56cc412a06df22178dac5c"},"source_status":"SOURCE_INDEXED","statement":"∀ {α : Type u} {l : List.{u} α} {a : α},\n  @Membership.mem.{u, u} α (List.{u} α) (@List.instMembership.{u} α) l a →\n    @Ne.{u + 1} (Option.{u} α) (@Option.some.{u} α a) (@List.getLast?.{u} α l) →\n      @Membership.mem.{u, u} α (List.{u} α) (@List.instMembership.{u} α) (@List.dropLast.{u} α l) a","statement_sha256":"50a8fb411d103e4102b8ba0e9444d4ed79590551bee62776b873b7cb7b5f10d4","verification_status":"NOT_CHECKED"},{"authority":"NONE","authorization":"NONE","current_applicability":"NOT_CHECKED","extensions":[],"freshness":"PINNED_HISTORICAL_SOURCE","kind":"theorem","object_contract_version":1,"object_id":"object-10ffbbb563c7cf9a56ab395cef916e883aa69da7d0b662db6a33b529332b0c21","qualified_name":"List.mem_dropLast_of_mem_of_ne_getLastD","source":{"commit":"d13f23b723b8a846827a245b89c10fc7d3f11612","module":"Mathlib.Data.List.Basic","path":"Mathlib/Data/List/Basic.lean","range":{"end":{"byte":14414,"column":50,"line":387},"start":{"byte":14242,"column":0,"line":385}},"repository":"https://github.com/leanprover-community/mathlib4","tree":"efa132418a56d0e38c56cc412a06df22178dac5c"},"source_status":"SOURCE_INDEXED","statement":"∀ {α : Type u} {l : List.{u} α} {a d : α},\n  @Membership.mem.{u, u} α (List.{u} α) (@List.instMembership.{u} α) l a →\n    @Ne.{u + 1} α a (@List.getLastD.{u} α l d) →\n      @Membership.mem.{u, u} α (List.{u} α) (@List.instMembership.{u} α) (@List.dropLast.{u} α l) a","statement_sha256":"6aa9c9adba5356e8b9263dec74ded2c3dfa5b40ca99d8a256bcb5fdb81509ce9","verification_status":"NOT_CHECKED"},{"authority":"NONE","authorization":"NONE","current_applicability":"NOT_CHECKED","extensions":[],"freshness":"PINNED_HISTORICAL_SOURCE","kind":"theorem","object_contract_version":1,"object_id":"object-44d188f46b50feafbb9f4ee0feb15a3efe49aeecd47065c30c58b41aa149c982","qualified_name":"List.mem_filter_of_mem","source":{"commit":"d13f23b723b8a846827a245b89c10fc7d3f11612","module":"Mathlib.Data.List.Basic","path":"Mathlib/Data/List/Basic.lean","range":{"end":{"byte":36841,"column":31,"line":972},"start":{"byte":36719,"column":0,"line":971}},"repository":"https://github.com/leanprover-community/mathlib4","tree":"efa132418a56d0e38c56cc412a06df22178dac5c"},"source_status":"SOURCE_INDEXED","statement":"∀ {α : Type u} {p : α → Bool} {a : α} {l : List.{u} α},\n  @Membership.mem.{u, u} α (List.{u} α) (@List.instMembership.{u} α) l a →\n    @Eq.{1} Bool (p a) Bool.true →\n      @Membership.mem.{u, u} α (List.{u} α) (@List.instMembership.{u} α) (@List.filter.{u} α p l) a","statement_sha256":"05aa2a257e8a05c10fa9a418f98cf1ddfa3830c83162016196aab58e46073da5","verification_status":"NOT_CHECKED"},{"authority":"NONE","authorization":"NONE","current_applicability":"NOT_CHECKED","extensions":[],"freshness":"PINNED_HISTORICAL_SOURCE","kind":"theorem","object_contract_version":1,"object_id":"object-0c0883a59f00cb0b60c73bd9452d1432743ad4c650297aaf7011bb76e158671a","qualified_name":"List.mem_getLast?_append_of_mem_getLast?","source":{"commit":"d13f23b723b8a846827a245b89c10fc7d3f11612","module":"Mathlib.Data.List.Basic","path":"Mathlib/Data/List/Basic.lean","range":{"end":{"byte":14067,"column":45,"line":379},"start":{"byte":13919,"column":0,"line":378}},"repository":"https://github.com/leanprover-community/mathlib4","tree":"efa132418a56d0e38c56cc412a06df22178dac5c"},"source_status":"SOURCE_INDEXED","statement":"∀ {α : Type u} {l₁ l₂ : List.{u} α} {x : α},\n  @Membership.mem.{u, u} α (Option.{u} α) (@Option.instMembership.{u} α) (@List.getLast?.{u} α l₂) x →\n    @Membership.mem.{u, u} α (Option.{u} α) (@Option.instMembership.{u} α)\n      (@List.getLast?.{u} α\n        (@HAppend.hAppend.{u, u, u} (List.{u} α) (List.{u} α) (List.{u} α)\n          (@instHAppendOfAppend.{u} (List.{u} α) (@List.instAppend.{u} α)) l₁ l₂))\n      x","statement_sha256":"3f23cbb9e55877d0f2f6862b1d9dd965e5cf81ad6c8afd76ce929a6f0f1dfc2a","verification_status":"NOT_CHECKED"},{"authority":"NONE","authorization":"NONE","current_applicability":"NOT_CHECKED","extensions":[],"freshness":"PINNED_HISTORICAL_SOURCE","kind":"theorem","object_contract_version":1,"object_id":"object-8cd6996fc35c2823ac1aba5a13ac7ee85a30c608e70495f309e519227ee87de7","qualified_name":"List.mem_getLast?_cons","source":{"commit":"d13f23b723b8a846827a245b89c10fc7d3f11612","module":"Mathlib.Data.List.Basic","path":"Mathlib/Data/List/Basic.lean","range":{"end":{"byte":12802,"column":18,"line":350},"start":{"byte":12651,"column":0,"line":348}},"repository":"https://github.com/leanprover-community/mathlib4","tree":"efa132418a56d0e38c56cc412a06df22178dac5c"},"source_status":"SOURCE_INDEXED","statement":"∀ {α : Type u} {x y : α} {l : List.{u} α},\n  @Membership.mem.{u, u} α (Option.{u} α) (@Option.instMembership.{u} α) (@List.getLast?.{u} α l) x →\n    @Membership.mem.{u, u} α (Option.{u} α) (@Option.instMembership.{u} α) (@List.getLast?.{u} α (@List.cons.{u} α y l))\n      x","statement_sha256":"a5b20529d7a4c214078cc67789db3cf29829b810eb84d154e6c65de3e42be171","verification_status":"NOT_CHECKED"},{"authority":"NONE","authorization":"NONE","current_applicability":"NOT_CHECKED","extensions":[],"freshness":"PINNED_HISTORICAL_SOURCE","kind":"theorem","object_contract_version":1,"object_id":"object-388548a36b9e3dc770677584acb723c6b07a2a1d0b65508353ac6ec246a9be9a","qualified_name":"List.mem_getLast?_eq_getLast","source":{"commit":"d13f23b723b8a846827a245b89c10fc7d3f11612","module":"Mathlib.Data.List.Basic","path":"Mathlib/Data/List/Basic.lean","range":{"end":{"byte":12418,"column":34,"line":341},"start":{"byte":12249,"column":0,"line":338}},"repository":"https://github.com/leanprover-community/mathlib4","tree":"efa132418a56d0e38c56cc412a06df22178dac5c"},"source_status":"SOURCE_INDEXED","statement":"∀ {α : Type u} {l : List.{u} α} {x : α},\n  @Membership.mem.{u, u} α (Option.{u} α) (@Option.instMembership.{u} α) (@List.getLast?.{u} α l) x →\n    ∃ (h : @Ne.{u + 1} (List.{u} α) l (@List.nil.{u} α)), @Eq.{u + 1} α x (@List.getLast.{u} α l h)","statement_sha256":"cddf6d0ea3f4c37e6a3268ee5e16b1bfe2aa8512be12bcc5c0fc2000f2128d4a","verification_status":"NOT_CHECKED"},{"authority":"NONE","authorization":"NONE","current_applicability":"NOT_CHECKED","extensions":[],"freshness":"PINNED_HISTORICAL_SOURCE","kind":"theorem","object_contract_version":1,"object_id":"object-7499ab70b312e4a00dd362fe53f09a02b04337d76410e047bc9953d0ef3f6555","qualified_name":"List.mem_head?_append_of_mem_head?","source":{"commit":"d13f23b723b8a846827a245b89c10fc7d3f11612","module":"Mathlib.Data.List.Basic","path":"Mathlib/Data/List/Basic.lean","range":{"end":{"byte":15908,"column":24,"line":431},"start":{"byte":15768,"column":0,"line":429}},"repository":"https://github.com/leanprover-community/mathlib4","tree":"efa132418a56d0e38c56cc412a06df22178dac5c"},"source_status":"SOURCE_INDEXED","statement":"∀ {α : Type u} {s t : List.{u} α} {x : α},\n  @Membership.mem.{u, u} α (Option.{u} α) (@Option.instMembership.{u} α) (@List.head?.{u} α s) x →\n    @Membership.mem.{u, u} α (Option.{u} α) (@Option.instMembership.{u} α)\n      (@List.head?.{u} α\n        (@HAppend.hAppend.{u, u, u} (List.{u} α) (List.{u} α) (List.{u} α)\n          (@instHAppendOfAppend.{u} (List.{u} α) (@List.instAppend.{u} α)) s t))\n      x","statement_sha256":"bcf7ab19102830f831cbef14d49adf6b08df79daf4e6615825dd4013793b32fd","verification_status":"NOT_CHECKED"},{"authority":"NONE","authorization":"NONE","current_applicability":"NOT_CHECKED","extensions":[],"freshness":"PINNED_HISTORICAL_SOURCE","kind":"theorem","object_contract_version":1,"object_id":"object-d472ad714f465dc699475833cd7f282325365834a975f26e31f2ecdf1846cd89","qualified_name":"List.mem_map_of_injective","source":{"commit":"d13f23b723b8a846827a245b89c10fc7d3f11612","module":"Mathlib.Data.List.Basic","path":"Mathlib/Data/List/Basic.lean","range":{"end":{"byte":2313,"column":86,"line":76},"start":{"byte":2091,"column":0,"line":73}},"repository":"https://github.com/leanprover-community/mathlib4","tree":"efa132418a56d0e38c56cc412a06df22178dac5c"},"source_status":"SOURCE_INDEXED","statement":"∀ {α : Type u} {β : Type v} {f : α → β},\n  @Function.Injective.{u + 1, v + 1} α β f →\n    ∀ {a : α} {l : List.{u} α},\n      Iff (@Membership.mem.{v, v} β (List.{v} β) (@List.instMembership.{v} β) (@List.map.{u, v} α β f l) (f a))\n        (@Membership.mem.{u, u} α (List.{u} α) (@List.instMembership.{u} α) l a)","statement_sha256":"10eca6baeb840a190cdbbd78536ac446e74bf64450a24019b089d100cd75a788","verification_status":"NOT_CHECKED"},{"authority":"NONE","authorization":"NONE","current_applicability":"NOT_CHECKED","extensions":[],"freshness":"PINNED_HISTORICAL_SOURCE","kind":"theorem","object_contract_version":1,"object_id":"object-d3dcf1dde976fe0805ef1d5d414f235e6f3d3c0f7d14e43d4b2c3e0e01c6b78a","qualified_name":"List.mem_map_of_involutive","source":{"commit":"d13f23b723b8a846827a245b89c10fc7d3f11612","module":"Mathlib.Data.List.Basic","path":"Mathlib/Data/List/Basic.lean","range":{"end":{"byte":2760,"column":82,"line":84},"start":{"byte":2587,"column":0,"line":83}},"repository":"https://github.com/leanprover-community/mathlib4","tree":"efa132418a56d0e38c56cc412a06df22178dac5c"},"source_status":"SOURCE_INDEXED","statement":"∀ {α : Type u} {f : α → α},\n  @Function.Involutive.{u + 1} α f →\n    ∀ {a : α} {l : List.{u} α},\n      Iff (@Membership.mem.{u, u} α (List.{u} α) (@List.instMembership.{u} α) (@List.map.{u, u} α α f l) a)\n        (@Membership.mem.{u, u} α (List.{u} α) (@List.instMembership.{u} α) l (f a))","statement_sha256":"5dc7db1ebaf94ee6fa8c087d53f85b0c44bed1bc6ad79e8a3c2403dea60dfedb","verification_status":"NOT_CHECKED"},{"authority":"NONE","authorization":"NONE","current_applicability":"NOT_CHECKED","extensions":[],"freshness":"PINNED_HISTORICAL_SOURCE","kind":"theorem","object_contract_version":1,"object_id":"object-088aef0b29aa28c24363805a04e8415bddbf0a99989e370605a4b0db6f582df2","qualified_name":"List.mem_of_mem_filter","source":{"commit":"d13f23b723b8a846827a245b89c10fc7d3f11612","module":"Mathlib.Data.List.Basic","path":"Mathlib/Data/List/Basic.lean","range":{"end":{"byte":36717,"column":24,"line":969},"start":{"byte":36618,"column":0,"line":968}},"repository":"https://github.com/leanprover-community/mathlib4","tree":"efa132418a56d0e38c56cc412a06df22178dac5c"},"source_status":"SOURCE_INDEXED","statement":"∀ {α : Type u} {p : α → Bool} {a : α} {l : List.{u} α},\n  @Membership.mem.{u, u} α (List.{u} α) (@List.instMembership.{u} α) (@List.filter.{u} α p l) a →\n    @Membership.mem.{u, u} α (List.{u} α) (@List.instMembership.{u} α) l a","statement_sha256":"5bac6c45ea6cf9b2c21ea0db09e5409bee08c99f4077c1e457bb16a98b6ccd1f","verification_status":"NOT_CHECKED"},{"authority":"NONE","authorization":"NONE","current_applicability":"NOT_CHECKED","extensions":[],"freshness":"PINNED_HISTORICAL_SOURCE","kind":"theorem","object_contract_version":1,"object_id":"object-d8e3b1f0c971fea6c061cd4825e68ca727200d81c8d4dcc4ddd61b0ea2fc8b8d","qualified_name":"List.mem_pair","source":{"commit":"d13f23b723b8a846827a245b89c10fc7d3f11612","module":"Mathlib.Data.List.Basic","path":"Mathlib/Data/List/Basic.lean","range":{"end":{"byte":2089,"column":30,"line":71},"start":{"byte":1990,"column":0,"line":70}},"repository":"https://github.com/leanprover-community/mathlib4","tree":"efa132418a56d0e38c56cc412a06df22178dac5c"},"source_status":"SOURCE_INDEXED","statement":"∀ {α : Type u} {a b c : α},\n  Iff\n    (@Membership.mem.{u, u} α (List.{u} α) (@List.instMembership.{u} α)\n      (@List.cons.{u} α b (@List.cons.{u} α c (@List.nil.{u} α))) a)\n    (Or (@Eq.{u + 1} α a b) (@Eq.{u + 1} α a c))","statement_sha256":"93e5e00978f0ae9be799c012ea5b14024ebb60287b131e0c295751f79eab884f","verification_status":"NOT_CHECKED"},{"authority":"NONE","authorization":"NONE","current_applicability":"NOT_CHECKED","extensions":[],"freshness":"PINNED_HISTORICAL_SOURCE","kind":"theorem","object_contract_version":1,"object_id":"object-b8f59a4471308e57d5f37da6c6a03cd9ef930ddb5068f6a2c244d46374caa994","qualified_name":"List.mem_pure","source":{"commit":"d13f23b723b8a846827a245b89c10fc7d3f11612","module":"Mathlib.Data.List.Basic","path":"Mathlib/Data/List/Basic.lean","range":{"end":{"byte":9506,"column":75,"line":254},"start":{"byte":9431,"column":0,"line":254}},"repository":"https://github.com/leanprover-community/mathlib4","tree":"efa132418a56d0e38c56cc412a06df22178dac5c"},"source_status":"SOURCE_INDEXED","statement":"∀ {α : Type u} (x y : α),\n  Iff\n    (@Membership.mem.{u, u} α (List.{u} α) (@List.instMembership.{u} α)\n      (@Pure.pure.{u, u} List.{u}\n        (@Applicative.toPure.{u, u} List.{u}\n          (@Alternative.toApplicative.{u, u} List.{u}\n            (@AlternativeMonad.toAlternative.{u, u} List.{u} List.instAlternativeMonad_mathlib.{u})))\n        α y)\n      x)\n    (@Eq.{u + 1} α x y)","statement_sha256":"dbd168283d0c1bd0c3d6b550026daca913d732bcbd249bb77a3b96e38aac778b","verification_status":"NOT_CHECKED"},{"authority":"NONE","authorization":"NONE","current_applicability":"NOT_CHECKED","extensions":[],"freshness":"PINNED_HISTORICAL_SOURCE","kind":"theorem","object_contract_version":1,"object_id":"object-0897e9fd72a8d5570c81ceb13c8637a99527b5289d1b8a7a8e9e845fec499e38","qualified_name":"List.mem_take_iff_idxOf_lt","source":{"commit":"d13f23b723b8a846827a245b89c10fc7d3f11612","module":"Mathlib.Data.List.Basic","path":"Mathlib/Data/List/Basic.lean","range":{"end":{"byte":22852,"column":7,"line":609},"start":{"byte":22672,"column":0,"line":606}},"repository":"https://github.com/leanprover-community/mathlib4","tree":"efa132418a56d0e38c56cc412a06df22178dac5c"},"source_status":"SOURCE_INDEXED","statement":"∀ {α : Type u} [inst : BEq.{u} α] [@LawfulBEq.{u} α inst] {a : α} {n : Nat} {l : List.{u} α},\n  @Membership.mem.{u, u} α (List.{u} α) (@List.instMembership.{u} α) l a →\n    Iff (@Membership.mem.{u, u} α (List.{u} α) (@List.instMembership.{u} α) (@List.take.{u} α n l) a)\n      (@LT.lt.{0} Nat instLTNat (@List.idxOf.{u} α inst a l) n)","statement_sha256":"f9c6ad9748a2f4860867d9a9e9260ec4c027085c61dbc3d8964c34a5197cd538","verification_status":"NOT_CHECKED"},{"authority":"NONE","authorization":"NONE","current_applicability":"NOT_CHECKED","extensions":[],"freshness":"PINNED_HISTORICAL_SOURCE","kind":"theorem","object_contract_version":1,"object_id":"object-f56b1b22d4cd7b3526862b32507dd055eda404ff15caaa8f42e8b6a0faf4cb6e","qualified_name":"List.monotone_filter_right","source":{"commit":"d13f23b723b8a846827a245b89c10fc7d3f11612","module":"Mathlib.Data.List.Basic","path":"Mathlib/Data/List/Basic.lean","range":{"end":{"byte":37011,"column":24,"line":978},"start":{"byte":36857,"column":0,"line":976}},"repository":"https://github.com/leanprover-community/mathlib4","tree":"efa132418a56d0e38c56cc412a06df22178dac5c"},"source_status":"SOURCE_INDEXED","statement":"∀ {α : Type u} (l : List.{u} α) ⦃p q : α → Bool⦄,\n  (∀ (a : α), @Eq.{1} Bool (p a) Bool.true → @Eq.{1} Bool (q a) Bool.true) →\n    @List.Sublist.{u} α (@List.filter.{u} α p l) (@List.filter.{u} α q l)","statement_sha256":"2831157010bf9968c27822594b6b1766089b5471f33e5828f86e42bf21048304","verification_status":"NOT_CHECKED"},{"authority":"NONE","authorization":"NONE","current_applicability":"NOT_CHECKED","extensions":[],"freshness":"PINNED_HISTORICAL_SOURCE","kind":"theorem","object_contract_version":1,"object_id":"object-11ec6c9cec8fa4bc7d8950b964fb0e56cdfc6a1ba826b3d2399a2da46b440c53","qualified_name":"List.notMem_of_subset","source":{"commit":"d13f23b723b8a846827a245b89c10fc7d3f11612","module":"Mathlib.Data.List.Basic","path":"Mathlib/Data/List/Basic.lean","range":{"end":{"byte":7099,"column":92,"line":194},"start":{"byte":7007,"column":0,"line":194}},"repository":"https://github.com/leanprover-community/mathlib4","tree":"efa132418a56d0e38c56cc412a06df22178dac5c"},"source_status":"SOURCE_INDEXED","statement":"∀ {α : Type u} {l l₁ : List.{u} α},\n  @HasSubset.Subset.{u} (List.{u} α) (@List.instHasSubset.{u} α) l l₁ → ∀ {a : α}, a ∉ l₁ → a ∉ l","statement_sha256":"0cd8288569bd89a616c27fc98d25f1dec7f4b7036f9943a3f898201230c7c01c","verification_status":"NOT_CHECKED"},{"authority":"NONE","authorization":"NONE","current_applicability":"NOT_CHECKED","extensions":[],"freshness":"PINNED_HISTORICAL_SOURCE","kind":"theorem","object_contract_version":1,"object_id":"object-b9bf90aebe054487ef18a785bd62f92da3645dfb4d28a51dc03136f0b17d736c","qualified_name":"List.of_mem_filter","source":{"commit":"d13f23b723b8a846827a245b89c10fc7d3f11612","module":"Mathlib.Data.List.Basic","path":"Mathlib/Data/List/Basic.lean","range":{"end":{"byte":36616,"column":85,"line":966},"start":{"byte":36531,"column":0,"line":966}},"repository":"https://github.com/leanprover-community/mathlib4","tree":"efa132418a56d0e38c56cc412a06df22178dac5c"},"source_status":"SOURCE_INDEXED","statement":"∀ {α : Type u} {p : α → Bool} {a : α} {l : List.{u} α},\n  @Membership.mem.{u, u} α (List.{u} α) (@List.instMembership.{u} α) (@List.filter.{u} α p l) a →\n    @Eq.{1} Bool (p a) Bool.true","statement_sha256":"42195b7605eed7ec67a3f6ea3fe3226ca904e779a90de281271da1932dabfe2d","verification_status":"NOT_CHECKED"},{"authority":"NONE","authorization":"NONE","current_applicability":"NOT_CHECKED","extensions":[],"freshness":"PINNED_HISTORICAL_SOURCE","kind":"theorem","object_contract_version":1,"object_id":"object-ff3e5c38f12ec6fea21ed328a3b6d40bc2133d05eb5157a08cd38990763466aa","qualified_name":"List.or_exists_of_exists_mem_cons","source":{"commit":"d13f23b723b8a846827a245b89c10fc7d3f11612","module":"Mathlib.Data.List.Basic","path":"Mathlib/Data/List/Basic.lean","range":{"end":{"byte":6077,"column":40,"line":167},"start":{"byte":5929,"column":0,"line":166}},"repository":"https://github.com/leanprover-community/mathlib4","tree":"efa132418a56d0e38c56cc412a06df22178dac5c"},"source_status":"SOURCE_INDEXED","statement":"∀ {α : Type u} {p : α → Prop} {a : α} {l : List.{u} α},\n  (∃ x, And (@Membership.mem.{u, u} α (List.{u} α) (@List.instMembership.{u} α) (@List.cons.{u} α a l) x) (p x)) →\n    Or (p a) (∃ x, And (@Membership.mem.{u, u} α (List.{u} α) (@List.instMembership.{u} α) l x) (p x))","statement_sha256":"5acda7386afab204f5f68713c991a5643bedb81004f7482bf918cabd4e8ed7af","verification_status":"NOT_CHECKED"},{"authority":"NONE","authorization":"NONE","current_applicability":"NOT_CHECKED","extensions":[],"freshness":"PINNED_HISTORICAL_SOURCE","kind":"theorem","object_contract_version":1,"object_id":"object-e3878e7b6d4bdd2835e647df2caed65c7f86f1ebd754453d312084f47d8cc9a9","qualified_name":"List.perm_reverse","source":{"commit":"d13f23b723b8a846827a245b89c10fc7d3f11612","module":"Mathlib.Data.List.Basic","path":"Mathlib/Data/List/Basic.lean","range":{"end":{"byte":10950,"column":43,"line":300},"start":{"byte":10798,"column":0,"line":298}},"repository":"https://github.com/leanprover-community/mathlib4","tree":"efa132418a56d0e38c56cc412a06df22178dac5c"},"source_status":"SOURCE_INDEXED","statement":"∀ {α : Type u} {l₁ l₂ : List.{u} α}, Iff (@List.Perm.{u} α l₁ (@List.reverse.{u} α l₂)) (@List.Perm.{u} α l₁ l₂)","statement_sha256":"0f1f7afc0e4c447441aaf5e08c7352ff3d2b283d71f89756abbf1bb75ebb79e7","verification_status":"NOT_CHECKED"},{"authority":"NONE","authorization":"NONE","current_applicability":"NOT_CHECKED","extensions":[],"freshness":"PINNED_HISTORICAL_SOURCE","kind":"theorem","object_contract_version":1,"object_id":"object-5fcf5979e0bbfa7a29a2d471c4febab5b9155411014ac32a0278d26f1a2638a6","qualified_name":"List.range'_0","source":{"commit":"d13f23b723b8a846827a245b89c10fc7d3f11612","module":"Mathlib.Data.List.Basic","path":"Mathlib/Data/List/Basic.lean","range":{"end":{"byte":44249,"column":55,"line":1186},"start":{"byte":44086,"column":0,"line":1182}},"repository":"https://github.com/leanprover-community/mathlib4","tree":"efa132418a56d0e38c56cc412a06df22178dac5c"},"source_status":"SOURCE_INDEXED","statement":"∀ (a b : Nat),\n  @Eq.{1} (List.{0} Nat) (List.range' a b (@OfNat.ofNat.{0} Nat (nat_lit 0) 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