Theorems · Definition · geometry

AffineEquiv.ofEq

{k : Type u_1} →
  {V₁ : Type u_2} →
    {P₁ : Type u_3} →
      [inst : Ring k] →
        [inst_1 : AddCommGroup V₁] →
          [inst_2 : Module k V₁] →
            [inst_3 : AddTorsor V₁ P₁] →
              (S₁ S₂ : AffineSubspace k P₁) →
                [inst_4 : Nonempty ↥S₁] → [inst_5 : Nonempty ↥S₂] → S₁ = S₂ → ↥S₁ ≃ᵃ[k] ↥S₂

Affine equivalence between two equal affine subspace. This is the affine version of LinearEquiv.ofEq.

Defined in

Mathlib.LinearAlgebra.AffineSpace.AffineSubspace.Basic

Cited by

4 results in Mathlib

Foundations

Depth 67 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

RingAddCommGroupModuleAddTorsorNonemptyNonempty