Theorems · Definition · group theory
MulEquiv.symm
{M : Type u_9} → {N : Type u_10} → [inst : Mul M] → [inst_1 : Mul N] → M ≃* N → N ≃* MThe inverse of an isomorphism is an isomorphism.
- Defined in
- Mathlib.Algebra.Group.Equiv.Defs
- Cited by
- 482 results in Mathlib
- Foundations
- Depth 15 from the axioms, rests on 73 definitions · uses Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites4
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Equiv.symmproof · cited by 3,681
- MulEquivstatement and proof · cited by 1,142
- MulEquiv.toEquivproof · cited by 126
- MulEquiv.symm_map_mulproof · cited by 3
Cited by601
Results whose statement or proof uses this declaration.
- RingEquiv.symmproof · cited by 567
- CoxeterSystem.simpleproof · cited by 73
- ConjAct.toConjActproof · cited by 56
- LinearEquiv.detproof · cited by 51
- OrderMonoidIso.symmproof · cited by 44
- MulEquiv.apply_symm_applystatement · cited by 37
- ContinuousMulEquiv.symmproof · cited by 27
- BialgEquiv.symmproof · cited by 21
- MulEquiv.symm_apply_applystatement · cited by 17
- Units.mapEquivproof · cited by 16
- QuotientGroup.congrproof · cited by 16
- StarMulEquiv.symmproof · cited by 14
Showing the 200 most cited of 601.