Theorems · Theorem · group theory
MulEquivClass.apply_mem_center_iff
∀ {M : Type u_3} {N : Type u_1} {F : Type u_2} [inst : EquivLike F M N] [inst_1 : Mul M] [inst_2 : Mul N]
[MulEquivClass F M N] (e : F) {x : M}, e x ∈ Set.center N ↔ x ∈ Set.center M- Defined in
- Mathlib.GroupTheory.Submonoid.Center
- Cited by
- 2 results in Mathlib
- Foundations
- Depth 19 from the axioms · uses propext, Quot.sound
- Assumes
- EquivLikeMulMulMulEquivClass
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites9
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
- Setstatement · cited by 53,352
- MulEquiv.symmproof · cited by 482
- EquivLikestatement and proof · cited by 165
- MulEquivClass.toMulEquivproof · cited by 57
- Set.centerstatement and proof · cited by 49
- MulEquivClassstatement and proof · cited by 30
- MulEquivClass.coe_symm_apply_applyproof · cited by 3
- MulEquivClass.apply_mem_centerproof · cited by 1
Cited by2
Results whose statement or proof uses this declaration.
- SpecialLinearGroup.mem_center_iffproof · cited by 2
- Algebra.IsCentral.of_algEquivproof · cited by 1