Theorems · Definition · geometry

AffineIsometryEquiv.trans

{𝕜 : Type u_1} →
  {V : Type u_2} →
    {V₂ : Type u_5} →
      {V₃ : Type u_6} →
        {P : Type u_10} →
          {P₂ : Type u_11} →
            {P₃ : Type u_12} →
              [inst : NormedField 𝕜] →
                [inst_1 : SeminormedAddCommGroup V] →
                  [inst_2 : NormedSpace 𝕜 V] →
                    [inst_3 : PseudoMetricSpace P] →
                      [inst_4 : NormedAddTorsor V P] →
                        [inst_5 : SeminormedAddCommGroup V₂] →
                          [inst_6 : NormedSpace 𝕜 V₂] →
                            [inst_7 : PseudoMetricSpace P₂] →
                              [inst_8 : NormedAddTorsor V₂ P₂] →
                                [inst_9 : SeminormedAddCommGroup V₃] →
                                  [inst_10 : NormedSpace 𝕜 V₃] →
                                    [inst_11 : PseudoMetricSpace P₃] →
                                      [inst_12 : NormedAddTorsor V₃ P₃] → (P ≃ᵃⁱ[𝕜] P₂) → (P₂ ≃ᵃⁱ[𝕜] P₃) → P ≃ᵃⁱ[𝕜] P₃

Composition of AffineIsometryEquivs as an AffineIsometryEquiv.

Defined in

Mathlib.Analysis.Normed.Affine.Isometry

Cited by

9 results in Mathlib

Foundations

Depth 49 from the axioms · uses propext, Quot.sound

Assumes

NormedFieldSeminormedAddCommGroupNormedSpacePseudoMetricSpaceNormedAddTorsorSeminormedAddCommGroupNormedSpacePseudoMetricSpaceNormedAddTorsorSeminormedAddCommGroupNormedSpacePseudoMetricSpaceNormedAddTorsor