Theorems · Definition · group theory
Submonoid.leftInvEquiv
{M : Type u_1} → [inst : CommMonoid M] → (S : Submonoid M) → S ≤ IsUnit.submonoid M → ↥S.leftInv ≃* ↥SThe submonoid of pointwise inverse of S is MulEquiv to S.
- Defined in
- Mathlib.GroupTheory.Submonoid.Inverses
- Cited by
- 9 results in Mathlib
- Foundations
- Depth 31 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.
Cites11
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- MonoidHomproof · cited by 3,629
- Submonoidstatement and proof · cited by 3,086
- CommMonoidstatement and proof · cited by 2,264
- Units.valproof · cited by 1,966
- MulEquivstatement · cited by 1,142
- IsUnit.unitproof · cited by 252
- MonoidHom.toOneHomproof · cited by 132
- OneHom.toFunproof · cited by 132
- IsUnit.submonoidstatement and proof · cited by 56
- Submonoid.leftInvstatement and proof · cited by 20
- Submonoid.fromCommLeftInvproof · cited by 2
Cited by10
Results whose statement or proof uses this declaration.
- Submonoid.leftInvEquiv_applystatement and proof · cited by 2
- Submonoid.mul_leftInvEquiv_symmstatement and proof · cited by 2
- IsLocalization.equivInvSubmonoidproof · cited by 1
- Submonoid.leftInvEquiv_mulstatement · cited by 1
- Submonoid.leftInvEquiv_symm_mulstatement and proof · cited by 1
- Submonoid.mul_leftInvEquivstatement · cited by 1
- Submonoid.leftInvEquiv_symm_eq_invstatement and proof · cited by 0
- Submonoid.leftInvEquiv_symm_fromLeftInvstatement and proof · cited by 0
- Submonoid.fromLeftInv_leftInvEquiv_symmstatement and proof · cited by 0
- Submonoid.leftInvEquiv.congr_simpstatement and proof · cited by 0