Theorems · Definition · geometry

AffineEquiv.affineSubspaceMap

{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 : AddCommGroup V₂] →
                [inst_3 : Module k V₁] →
                  [inst_4 : Module k V₂] →
                    [inst_5 : AddTorsor V₁ P₁] →
                      [inst_6 : AddTorsor V₂ P₂] →
                        (e : P₁ ≃ᵃ[k] P₂) →
                          (s : AffineSubspace k P₁) → [inst_7 : Nonempty ↥s] → ↥s ≃ᵃ[k] ↥(AffineSubspace.map (↑e) s)

An affine equivalence restricts to an affine equivalence between an affine subspace and its image.

Defined in

Mathlib.LinearAlgebra.AffineSpace.Restrict

Cited by

2 results in Mathlib

Foundations

Depth 72 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

RingAddCommGroupAddCommGroupModuleModuleAddTorsorAddTorsorNonempty