Theorems · Definition · geometry

AffineEquiv.prodComm

(k : Type u_1) →
  (P₁ : Type u_2) →
    (P₂ : Type u_3) →
      {V₁ : Type u_6} →
        {V₂ : Type u_7} →
          [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] → P₁ × P₂ ≃ᵃ[k] P₂ × P₁

Product of affine spaces is commutative up to affine isomorphism.

Defined in

Mathlib.LinearAlgebra.AffineSpace.AffineEquiv

Cited by

4 results in Mathlib

Foundations

Depth 28 from the axioms · uses propext, Quot.sound

Assumes

RingAddCommGroupAddCommGroupModuleModuleAddTorsorAddTorsor