Theorems · Theorem · group theory

AddAction.IsPreprimitive.of_isTrivialBlock_base

∀ {G : Type u_1} {X : Type u_2} [inst : AddGroup G] [inst_1 : AddAction G X] [AddAction.IsPretransitive G X] (a : X),
  (∀ {B : Set X}, a ∈ B → AddAction.IsBlock G B → AddAction.IsTrivialBlock B) → AddAction.IsPreprimitive G X

If the action is pretransitive, then the trivial blocks condition implies preprimitivity (based condition)

Defined in

Mathlib.GroupTheory.GroupAction.Primitive

Cited by

1 results in Mathlib

Foundations

Depth 72 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

AddGroupAddActionAddAction.IsPretransitive