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@Function.Injective.{u_4 + 1, u_5} α β f →\n    @Function.IsPartialInv.{u_4, u_5} α β f (@Function.partialInv.{u_4, u_5} α β f)","statement_sha256":"5e0c98ae5521f9bdcb8718fc484e2943d4d632ffb641dc20b75d60d85d989346","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-e439eaf26ca9346097f0e9d5f56a7df4eb629bd369e716c99010fe367e34d110","qualified_name":"Function.Injective.isPartialOrder_onFun","source":{"commit":"d13f23b723b8a846827a245b89c10fc7d3f11612","module":"Mathlib.Logic.Function.Basic","path":"Mathlib/Logic/Function/Basic.lean","range":{"end":{"byte":3148,"column":32,"line":103},"start":{"byte":2998,"column":0,"line":101}},"repository":"https://github.com/leanprover-community/mathlib4","tree":"efa132418a56d0e38c56cc412a06df22178dac5c"},"source_status":"SOURCE_INDEXED","statement":"∀ {α : Sort u_1} {β 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@Function.Surjective.{imax u_2 u_3, imax u_1 u_3} (β → γ) (α → γ) fun g =>\n        @Function.comp.{u_1, u_2, u_3} α β γ g f","statement_sha256":"220e3da9dfa5e3bad71a13579886f4d0620053866974022c78903a73ebb68b6c","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-d57266f3308e97ea64c84ee71e6cb2138dfb2a3a5a7c7a9bd0782a4569b6738e","qualified_name":"Function.Injective.trichotomous_onFun","source":{"commit":"d13f23b723b8a846827a245b89c10fc7d3f11612","module":"Mathlib.Logic.Function.Basic","path":"Mathlib/Logic/Function/Basic.lean","range":{"end":{"byte":2868,"column":87,"line":94},"start":{"byte":2664,"column":0,"line":92}},"repository":"https://github.com/leanprover-community/mathlib4","tree":"efa132418a56d0e38c56cc412a06df22178dac5c"},"source_status":"SOURCE_INDEXED","statement":"∀ {α : Sort u_1} {β : Sort 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[Function.HasUncurry.{u_2, u_3, u_4} β γ δ] →\n          Function.HasUncurry.{max u_1 u_2, max u_3 u_1, u_4} (α → β) (Prod.{u_1, u_3} α γ) δ","statement_sha256":"434ac3786a6cf448770747797f248fa68fdc45f796ee751636e92f5e12bab6c0","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-44cd7d7ae45e647befc41fd3c11ea455e4c13ea2dd2647f0e6942f4315305f30","qualified_name":"Function.hfunext","source":{"commit":"d13f23b723b8a846827a245b89c10fc7d3f11612","module":"Mathlib.Logic.Function.Basic","path":"Mathlib/Logic/Function/Basic.lean","range":{"end":{"byte":4077,"column":7,"line":128},"start":{"byte":3725,"column":0,"line":122}},"repository":"https://github.com/leanprover-community/mathlib4","tree":"efa132418a56d0e38c56cc412a06df22178dac5c"},"source_status":"SOURCE_INDEXED","statement":"∀ {α α' : Sort u} {β : α → 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α → β} {γ : Type u_4} [Nontrivial.{u_4} γ],\n  Iff\n    (@Function.Injective.{max u_2 (u_4 + 1), max u_1 (u_4 + 1)} (β → γ) (α → γ) fun g =>\n      @Function.comp.{u_1, u_2, u_4 + 1} α β γ g f)\n    (@Function.Surjective.{u_1, u_2} α β 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@Eq.{imax (max (u_1 + 1) (u_2 + 1)) u_3} (Prod.{u_2, u_1} β α → γ)\n    (@Function.uncurry.{u_2, u_1, u_3} β α γ (@flip.{u_1 + 1, u_2 + 1, u_3} α β γ f))\n    (@Function.comp.{max (u_1 + 1) (u_2 + 1), max (u_2 + 1) (u_1 + 1), u_3} (Prod.{u_2, u_1} β α) (Prod.{u_1, u_2} α β)\n      γ (@Function.uncurry.{u_1, u_2, u_3} α β γ f) (@Prod.swap.{u_2, u_1} β 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@LE.le.{max u_3 u_4} (Set.{max u_3 u_4} (α → β)) (@Set.instLE.{max u_3 u_4} (α → β)) A B →\n    @Set.SeparatesPoints.{u_3, u_4} α β A → @Set.SeparatesPoints.{u_3, u_4} α β 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(∀ (a : α), @ExistsUnique.{u_1} α fun b => r a b)\n    (∃ f, And (@Function.Involutive.{u_1} α f) (@Eq.{max 1 u_1} (α → α → Prop) r fun x1 x2 => @Eq.{u_1} α (f x1) 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