Theorems · Theorem · group theory

SubAddAction.ofStabilizer.isPretransitive_iff

∀ {G : Type u_1} {α : Type u_2} [inst : AddGroup G] [inst_1 : AddAction G α] [AddAction.IsPretransitive G α] {a b : α},
  AddAction.IsPretransitive ↥(AddAction.stabilizer G a) ↥(SubAddAction.ofStabilizer G a) ↔
    AddAction.IsPretransitive ↥(AddAction.stabilizer G b) ↥(SubAddAction.ofStabilizer G b)

Defined in: Mathlib.GroupTheory.GroupAction.MultipleTransitivity
Cited by: 0 results in Mathlib
Foundations: Depth 36 from the axioms · uses propext, Classical.choice, Quot.sound
Assumes: AddGroup AddAction AddAction.IsPretransitive

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AddGroupstatement and proof · cited by 4,410
AddSubgroupstatement · cited by 3,232
HVAdd.hVAddproof · cited by 1,820
AddActionstatement and proof · cited by 820
AddAction.stabilizerstatement and proof · cited by 112
SubAddActionstatement · cited by 86
AddAction.IsPretransitivestatement and proof · cited by 56
SubAddAction.ofStabilizerstatement and proof · cited by 29
AddAction.exists_vadd_eqproof · cited by 20
SubAddAction.ofStabilizer.isPretransitive_iff_of_addConjproof · cited by 1

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