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Theorems · Theorem · group theory

Submonoid.mul_leftInvEquiv

∀ {M : Type u_1} [inst : CommMonoid M] (S : Submonoid M) (hS : S ≤ IsUnit.submonoid M) (x : ↥S.leftInv),
  ↑x * ↑((S.leftInvEquiv hS) x) = 1
Defined in
Mathlib.GroupTheory.Submonoid.Inverses
Cited by
1 results in Mathlib
Foundations
Depth 33 from the axioms · uses propext, Classical.choice, Quot.sound
Assumes
CommMonoid
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Around this declaration

Dashed lines are statement dependencies; solid lines are citations in proofs.

Submonoid.leftInvEquiv_symm_mul · cited by 1Submonoid.leftInvEquiv_sy…DFunLike.coe · cited by 62936DFunLike.coeSubmonoid · cited by 3086SubmonoidCommMonoid · cited by 2264CommMonoidMulEquiv · cited by 1142MulEquivIsUnit.submonoid · cited by 56IsUnit.submonoidSubmonoid.leftInv · cited by 20Submonoid.leftInvSubmonoid.leftInvEquiv · cited by 9Submonoid.leftInvEquivSubmonoid.mul_fromLeftInv · cited by 5Submonoid.mul_fromLeftInvSubmonoid.leftInvEquiv_apply · cited by 2Submonoid.leftInvEquiv_ap…Submonoid.mul_leftInvEquivCITED BYCITES

Cites9

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Cited by1

Results whose statement or proof uses this declaration.