Theorems · Theorem · group theory
Submonoid.leftInvEquiv_symm_eq_inv
∀ {M : Type u_1} [inst : CommGroup M] (S : Submonoid M) (hS : S ≤ IsUnit.submonoid M) (x : ↥S),
↑((S.leftInvEquiv hS).symm x) = (↑x)⁻¹- Defined in
- Mathlib.GroupTheory.Submonoid.Inverses
- Cited by
- 0 results in Mathlib
- Foundations
- Depth 35 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- CommGroup
Around this declaration
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Cites11
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
- MulEquivstatement · cited by 1,142
- CommGroupstatement and proof · cited by 990
- MulEquiv.symmstatement and proof · cited by 482
- mul_inv_cancelproof · cited by 128
- IsUnit.submonoidstatement and proof · cited by 56
- Submonoid.leftInvstatement · cited by 20
- mul_right_injproof · cited by 11
- Submonoid.leftInvEquivstatement and proof · cited by 9
- Submonoid.mul_leftInvEquiv_symmproof · cited by 2
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