Theorems · Theorem · group theory

MulAction.IsPreprimitive.of_isTrivialBlock_base

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

GroupMulActionMulAction.IsPretransitive