Theorems · Theorem · group theory

SubMulAction.ofStabilizer.isPretransitive_iff_of_conj

∀ {G : Type u_1} {α : Type u_2} [inst : Group G] [inst_1 : MulAction G α] {a b : α} {g : G},
  b = g • a →
    (MulAction.IsPretransitive ↥(MulAction.stabilizer G a) ↥(SubMulAction.ofStabilizer G a) ↔
      MulAction.IsPretransitive ↥(MulAction.stabilizer G b) ↥(SubMulAction.ofStabilizer G b))

Defined in: Mathlib.GroupTheory.GroupAction.MultipleTransitivity
Cited by: 1 results in Mathlib
Foundations: Depth 34 from the axioms · uses propext, Classical.choice, Quot.sound
Assumes: Group MulAction

Mathlib docs Source Loogle LeanSearch

Around this declaration

Dashed lines are statement dependencies; solid lines are citations in proofs.

Cites11

Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.

Groupstatement and proof · cited by 6,238
Subgroupstatement · cited by 3,593
MulActionstatement and proof · cited by 1,294
MulAction.stabilizerstatement · cited by 254
SubMulActionstatement · cited by 120
MulAction.IsPretransitivestatement · cited by 94
MulEquiv.surjectiveproof · cited by 41
SubMulAction.ofStabilizerstatement · cited by 33
MulAction.stabilizerEquivStabilizerproof · cited by 16
MulAction.isPretransitive_congrproof · cited by 4
SubMulAction.ofStabilizer.conjMap_bijectiveproof · cited by 2

Cited by1

Results whose statement or proof uses this declaration.

SubMulAction.ofStabilizer.isPretransitive_iffproof · cited by 0