Theorems · Theorem · group theory

AddAction.isPreprimitive_ofFixingAddSubgroup_addConj_iff

∀ {G : Type u_1} [inst : AddGroup G] {α : Type u_2} [inst_1 : AddAction G α] {s : Set α} {g : G},
  AddAction.IsPreprimitive ↥(fixingAddSubgroup G s) ↥(SubAddAction.ofFixingAddSubgroup G s) ↔
    AddAction.IsPreprimitive ↥(fixingAddSubgroup G (g +ᵥ s)) ↥(SubAddAction.ofFixingAddSubgroup G (g +ᵥ s))

Defined in: Mathlib.GroupTheory.GroupAction.MultiplePrimitivity
Cited by: 1 results in Mathlib
Foundations: Depth 64 from the axioms · uses propext, Classical.choice, Quot.sound
Assumes: AddGroup AddAction

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Cites14

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

Setstatement and proof · cited by 53,352
AddGroupstatement and proof · cited by 4,410
AddSubgroupstatement · cited by 3,232
HVAdd.hVAddstatement · cited by 1,820
AddActionstatement and proof · cited by 820
Set.vaddSetstatement · cited by 403
SubAddActionstatement · cited by 86
fixingAddSubgroupstatement · cited by 50
AddEquiv.surjectiveproof · cited by 37
SubAddAction.ofFixingAddSubgroupstatement · cited by 32
AddAction.IsPreprimitivestatement · cited by 25
AddAction.isPreprimitive_congrproof · cited by 4

Cited by1

Results whose statement or proof uses this declaration.

AddAction.isMultiplyPreprimitive_succ_iff_ofStabilizerproof · cited by 0