Theorems · Theorem · group theory

MulAction.IsBlock.smul_eq_of_mem

∀ {G : Type u_1} [inst : Group G] {X : Type u_2} [inst_1 : MulAction G X] {B : Set X},
  MulAction.IsBlock G B → ∀ ⦃g : G⦄ ⦃a : X⦄, a ∈ B → g • a ∈ B → g • B = B

Alias of the forward direction of MulAction.isBlock_iff_smul_eq_of_mem.

Defined in

Mathlib.GroupTheory.GroupAction.Blocks

Cited by

1 results in Mathlib

Foundations

Depth 68 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

GroupMulAction