Theorems · Theorem · group theory
MulEquivClass.coe_symm_apply_apply
∀ {α : Type u_9} {β : Type u_10} [inst : Mul α] [inst_1 : Mul β] {F : Type u_11} [inst_2 : EquivLike F α β]
[inst_3 : MulEquivClass F α β] (e : F) (x : α), (↑e).symm (e x) = x- Defined in
- Mathlib.Algebra.Group.Equiv.Defs
- Cited by
- 3 results in Mathlib
- Foundations
- Depth 17 from the axioms · uses Quot.sound
- Assumes
- MulMulEquivLikeMulEquivClass
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites8
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- DFunLike.coestatement · cited by 62,936
- MulEquivstatement · cited by 1,142
- MulEquiv.symmstatement · cited by 482
- EquivLikestatement and proof · cited by 165
- MulEquiv.toEquivproof · cited by 126
- Equiv.left_invproof · cited by 59
- MulEquivClass.toMulEquivstatement and proof · cited by 57
- MulEquivClassstatement and proof · cited by 30
Cited by3
Results whose statement or proof uses this declaration.
- MulEquivClass.apply_mem_center_iffproof · cited by 2
- map_dvd_iff_dvd_symmproof · cited by 0
- Submonoid.IsLocalizationMap.mulEquiv_compproof · cited by 0