Theorems · Theorem · group theory

SubAddAction.ofStabilizer.isPretransitive_iff_of_addConj

∀ {G : Type u_1} {α : Type u_2} [inst : AddGroup G] [inst_1 : AddAction G α] {a b : α} {g : G},
  b = g +ᵥ a →
    (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: 1 results in Mathlib
Foundations: Depth 35 from the axioms · uses propext, Classical.choice, Quot.sound
Assumes: AddGroup AddAction

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Cites12

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

AddGroupstatement and proof · cited by 4,410
AddSubgroupstatement · cited by 3,232
HVAdd.hVAddstatement and proof · cited by 1,820
AddActionstatement and proof · cited by 820
AddAction.stabilizerstatement · cited by 112
SubAddActionstatement · cited by 86
AddAction.IsPretransitivestatement · cited by 56
AddEquiv.surjectiveproof · cited by 37
SubAddAction.ofStabilizerstatement · cited by 29
AddAction.stabilizerEquivStabilizerproof · cited by 16
AddAction.isPretransitive_congrproof · cited by 4
SubAddAction.ofStabilizer.addConjMap_bijectiveproof · cited by 2

Cited by1

Results whose statement or proof uses this declaration.

SubAddAction.ofStabilizer.isPretransitive_iffproof · cited by 0