Theorems · Theorem · geometry

AffineMap.span_eq_top_of_surjective

∀ {k : Type u_1} {V₁ : Type u_2} {P₁ : Type u_3} {V₂ : Type u_4} {P₂ : Type u_5} [inst : Ring k]
  [inst_1 : AddCommGroup V₁] [inst_2 : Module k V₁] [inst_3 : AddTorsor V₁ P₁] [inst_4 : AddCommGroup V₂]
  [inst_5 : Module k V₂] [inst_6 : AddTorsor V₂ P₂] (f : P₁ →ᵃ[k] P₂) {s : Set P₁},
  Function.Surjective ⇑f → affineSpan k s = ⊤ → affineSpan k (⇑f '' s) = ⊤

Defined in

Mathlib.LinearAlgebra.AffineSpace.AffineSubspace.Basic

Cited by

1 results in Mathlib

Foundations

Depth 66 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

RingAddCommGroupModuleAddTorsorAddCommGroupModuleAddTorsor