div_eq_iff_eq_mul

Exact source identity

Canonical occurrence

object-eea527d123fd961af8a1de5e71e191be43714a584f0fd68709bf7cfcdf76cf8c

Kind

theorem

Module

Mathlib.Algebra.Group.Basic

Path

Mathlib/Algebra/Group/Basic.lean

Repository

https://github.com/leanprover-community/mathlib4

Commit

d13f23b723b8a846827a245b89c10fc7d3f11612

Tree

efa132418a56d0e38c56cc412a06df22178dac5c

Statement digest

f63abd57d9159a848a175bb4f125685ea86de2fd050ca3a4a63a506d4ac326f2

Source range

772:0–773:100

Open exact source occurrence

Indexed statement

∀ {G : Type u_3} [inst : Group.{u_3} G] {a b c : G},
  Iff
    (@Eq.{u_3 + 1} G
      (@HDiv.hDiv.{u_3, u_3, u_3} G G G
        (@instHDiv.{u_3} G (@DivInvMonoid.toDiv.{u_3} G (@Group.toDivInvMonoid.{u_3} G inst))) a b)
      c)
    (@Eq.{u_3 + 1} G a
      (@HMul.hMul.{u_3, u_3, u_3} G G G
        (@instHMul.{u_3} G
          (@MulOne.toMul.{u_3} G
            (@MulOneClass.toMulOne.{u_3} G
              (@Monoid.toMulOneClass.{u_3} G (@DivInvMonoid.toMonoid.{u_3} G (@Group.toDivInvMonoid.{u_3} G inst))))))
        c b))

This text is bound to the statement digest above. Parsing and indexing it does not establish proof validity, informal fidelity, implication or equivalence.

Independent status axes

Source status

SOURCE_INDEXED

Independent verification

NOT_CHECKED

Current applicability

NOT_CHECKED

Freshness

PINNED_HISTORICAL_SOURCE

Action authorization

NONE

Lifecycle and research maturity are UNKNOWN in this source catalogue. The source pin is historical; absence of a newer change or revocation has not been checked.

Declared structural neighborhood

1 incoming and 0 outgoing relations occur in the bounded projection below. DECLARES, IMPORTS_MODULE and TYPE_REFERENCES are structural source relations only. Each explicitly sets logical implication and semantic equivalence to false.

Omitted structural references

• DivInvMonoid.toDiv — named target outside this selected catalogue slice
• DivInvMonoid.toMonoid — named target outside this selected catalogue slice
• Eq — named target outside this selected catalogue slice
• Group — named target outside this selected catalogue slice
• Group.toDivInvMonoid — named target outside this selected catalogue slice
• HDiv.hDiv — named target outside this selected catalogue slice
• HMul.hMul — named target outside this selected catalogue slice
• Iff — named target outside this selected catalogue slice
• Monoid.toMulOneClass — named target outside this selected catalogue slice
• MulOne.toMul — named target outside this selected catalogue slice
• MulOneClass.toMulOne — named target outside this selected catalogue slice
• instHDiv — named target outside this selected catalogue slice
• instHMul — named target outside this selected catalogue slice

Module declarations omitted

93

Module imports omitted

8

Module type references omitted

5635

Omissions are preserved rather than converted into absent relations. Out-of-slice targets remain unsupported by this projection.

Independent validation

Validate the committed catalogue, pins, canonical encoding, identities, relation endpoints, named omissions and authority ceiling from a clean checkout:

python3 -I -S -B conformance/source_catalogue_v1/consumer.py \
  --catalogue-root website/public/catalogues/mathlib/v4.34.1 \
  --policy conformance/source_catalogue_v1/trust-policy.json \
  --policy-sha256 c3cdec2b2c784728621bb8c25a055a1e73d67d3c1c922b7ab62b09003399e1c9 \
  --audit-imports

Manifest · Module shard · Search export

This replay does not fetch Mathlib, rerun Lean, authenticate GitHub, check current applicability, or grant action authority. It validates the pinned publication contract and returns only its bounded source-indexing result.