Theorems · Theorem · group theory

SubMulAction.ofStabilizer.isPretransitive_iff

∀ {G : Type u_1} {α : Type u_2} [inst : Group G] [inst_1 : MulAction G α] [MulAction.IsPretransitive G α] {a b : α},
  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: 0 results in Mathlib
Foundations: Depth 35 from the axioms · uses propext, Classical.choice, Quot.sound
Assumes: Group MulAction MulAction.IsPretransitive

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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 and proof · cited by 254
SubMulActionstatement · cited by 120
MulAction.IsPretransitivestatement and proof · cited by 94
SubMulAction.ofStabilizerstatement and proof · cited by 33
MulAction.exists_smul_eqproof · cited by 32
SubMulAction.ofStabilizer.isPretransitive_iff_of_conjproof · cited by 1

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