Theorems · Theorem · group theory

AddAction.isPreprimitive_fixingAddSubgroup_insert_iff

∀ {G : Type u_1} [inst : AddGroup G] {α : Type u_2} [inst_1 : AddAction G α] {a : α}
  {t : Set ↥(SubAddAction.ofStabilizer G a)},
  AddAction.IsPreprimitive ↥(fixingAddSubgroup G (insert a (Subtype.val '' t)))
      ↥(SubAddAction.ofFixingAddSubgroup G (insert a (Subtype.val '' t))) ↔
    AddAction.IsPreprimitive ↥(fixingAddSubgroup (↥(AddAction.stabilizer G a)) t)
      ↥(SubAddAction.ofFixingAddSubgroup (↥(AddAction.stabilizer G a)) t)

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

AddGroupAddAction