Theorems · Theorem · geometry

vectorSpan_prod_eq

∀ {k : Type u_1} {V : Type u_2} {W : Type u_3} {P : Type u_4} {Q : Type u_5} [inst : Ring k] [inst_1 : AddCommGroup V]
  [inst_2 : Module k V] [inst_3 : AddTorsor V P] [inst_4 : AddCommGroup W] [inst_5 : Module k W]
  [inst_6 : AddTorsor W Q] {s : Set P} {t : Set Q},
  s.Nonempty → t.Nonempty → vectorSpan k (s ×ˢ t) = (vectorSpan k s).prod (vectorSpan k t)

Defined in

Mathlib.LinearAlgebra.AffineSpace.AffineSubspace.Basic

Cited by

2 results in Mathlib

Foundations

Depth 31 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

RingAddCommGroupModuleAddTorsorAddCommGroupModuleAddTorsor