Theorems · Definition · geometry

AffineEquiv.trans

{k : Type u_1} →
  {P₁ : Type u_2} →
    {P₂ : Type u_3} →
      {P₃ : Type u_4} →
        {V₁ : Type u_6} →
          {V₂ : Type u_7} →
            {V₃ : Type u_8} →
              [inst : Ring k] →
                [inst_1 : AddCommGroup V₁] →
                  [inst_2 : AddCommGroup V₂] →
                    [inst_3 : AddCommGroup V₃] →
                      [inst_4 : Module k V₁] →
                        [inst_5 : Module k V₂] →
                          [inst_6 : Module k V₃] →
                            [inst_7 : AddTorsor V₁ P₁] →
                              [inst_8 : AddTorsor V₂ P₂] →
                                [inst_9 : AddTorsor V₃ P₃] → (P₁ ≃ᵃ[k] P₂) → (P₂ ≃ᵃ[k] P₃) → P₁ ≃ᵃ[k] P₃

Composition of two AffineEquivalences, applied left to right.

Defined in

Mathlib.LinearAlgebra.AffineSpace.AffineEquiv

Cited by

11 results in Mathlib

Foundations

Depth 34 from the axioms · uses propext, Quot.sound

Assumes

RingAddCommGroupAddCommGroupAddCommGroupModuleModuleModuleAddTorsorAddTorsorAddTorsor