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Theorems · Theorem · group theory

Submonoid.mul_fromLeftInv

∀ {M : Type u_1} [inst : Monoid M] (S : Submonoid M) (x : ↥S.leftInv), ↑x * ↑(S.fromLeftInv x) = 1
Defined in
Mathlib.GroupTheory.Submonoid.Inverses
Cited by
5 results in Mathlib
Foundations
Depth 20 from the axioms · uses propext, Classical.choice
Assumes
Monoid
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Around this declaration

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

Submonoid.fromLeftInv_mul · cited by 1Submonoid.fromLeftInv_mulSubmonoid.mul_leftInvEquiv · cited by 1Submonoid.mul_leftInvEquivSubmonoid.fromLeftInv_eq_iff · cited by 0Submonoid.fromLeftInv_eq_…Submonoid.fromLeftInv_eq_inv · cited by 0Submonoid.fromLeftInv_eq_…Submonoid.fromLeftInv_one · cited by 0Submonoid.fromLeftInv_oneMonoid · cited by 3887MonoidSubmonoid · cited by 3086SubmonoidSubtype.prop · cited by 505Subtype.propSubmonoid.leftInv · cited by 20Submonoid.leftInvSubmonoid.fromLeftInv · cited by 8Submonoid.fromLeftInvSubmonoid.mul_fromLeftInvCITED BYCITES

Cites5

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Cited by5

Results whose statement or proof uses this declaration.