Theorems · Theorem · geometry

AffineSubspace.smul_mem_smul_iff

∀ {k : Type u_2} {V : Type u_3} [inst : Ring k] [inst_1 : AddCommGroup V] [inst_2 : Module k V] {s : AffineSubspace k V}
  {p : V} {G : Type u_9} [inst_3 : Group G] [inst_4 : DistribMulAction G V] [inst_5 : SMulCommClass G k V] {a : G},
  a • p ∈ a • s ↔ p ∈ s

Defined in

Mathlib.LinearAlgebra.AffineSpace.Pointwise

Cited by

1 results in Mathlib

Foundations

Depth 32 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

RingAddCommGroupModuleGroupDistribMulActionSMulCommClass