Theorems · Definition · group theory
SubMulAction.fixingSubgroupEquivFixingSubgroup
{M : Type u_1} →
{α : Type u_2} →
[inst : Group M] →
[inst_1 : MulAction M α] → {s t : Set α} → {g : M} → g • t = s → ↥(fixingSubgroup M t) ≃* ↥(fixingSubgroup M s)The equivalence of fixingSubgroup M t with fixingSubgroup M s
when s is a translate of t.
- Cited by
- 5 results in Mathlib
- Foundations
- Depth 34 from the axioms · uses propext, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites13
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- DFunLike.coeproof · cited by 62,936
- Setstatement and proof · cited by 53,352
- Groupstatement and proof · cited by 6,238
- Subgroupstatement · cited by 3,593
- MulActionstatement and proof · cited by 1,294
- MulEquivstatement · cited by 1,142
- Set.smulSetstatement · cited by 608
- fixingSubgroupstatement and proof · cited by 83
- MulAut.conjproof · cited by 64
- MulEquiv.transproof · cited by 53
- MulEquiv.subgroupCongrproof · cited by 10
- MulEquiv.subgroupMapproof · cited by 4
Cited by6
Results whose statement or proof uses this declaration.
- SubMulAction.conjMap_ofFixingSubgroupstatement · cited by 2
- SubMulAction.conjMap_ofFixingSubgroup_bijectivestatement · cited by 1
- MulAction.isPreprimitive_ofFixingSubgroup_conj_iffproof · cited by 1
- SubMulAction.fixingSubgroupEquivFixingSubgroup_coe_applystatement · cited by 0
- SubMulAction.fixingSubgroupEquivFixingSubgroup.congr_simpstatement and proof · cited by 0
- SubMulAction.conjMap_ofFixingSubgroup_coe_applystatement · cited by 0