Theorems · Theorem · group theory
Submonoid.mul_leftInvEquiv_symm
∀ {M : Type u_1} [inst : CommMonoid M] (S : Submonoid M) (hS : S ≤ IsUnit.submonoid M) (x : ↥S),
↑x * ↑((S.leftInvEquiv hS).symm x) = 1- Defined in
- Mathlib.GroupTheory.Submonoid.Inverses
- Cited by
- 2 results in Mathlib
- Foundations
- Depth 34 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- CommMonoid
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites10
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- DFunLike.coestatement and proof · cited by 62,936
- Submonoidstatement and proof · cited by 3,086
- CommMonoidstatement and proof · cited by 2,264
- MulEquivstatement · cited by 1,142
- MulEquiv.symmstatement and proof · cited by 482
- IsUnit.submonoidstatement and proof · cited by 56
- MulEquiv.apply_symm_applyproof · cited by 37
- Submonoid.leftInvstatement · cited by 20
- Submonoid.leftInvEquivstatement and proof · cited by 9
- Submonoid.leftInvEquiv_mulproof · cited by 1
Cited by2
Results whose statement or proof uses this declaration.
- IsLocalization.mul_toInvSubmonoidproof · cited by 2
- Submonoid.leftInvEquiv_symm_eq_invproof · cited by 0