Theorems · Theorem · geometry

AffineSubspace.smul_mem_smul_iff_of_isUnit

∀ {M : Type u_1} {k : Type u_2} {V : Type u_3} [inst : Ring k] [inst_1 : AddCommGroup V] [inst_2 : Module k V]
  [inst_3 : Monoid M] [inst_4 : DistribMulAction M V] [inst_5 : SMulCommClass M k V] {a : M} {s : AffineSubspace k V}
  {p : V}, IsUnit a → (a • p ∈ a • s ↔ p ∈ s)

Defined in

Mathlib.LinearAlgebra.AffineSpace.Pointwise

Cited by

1 results in Mathlib

Foundations

Depth 33 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

RingAddCommGroupModuleMonoidDistribMulActionSMulCommClass