Theorems · Theorem · geometry

AffineIsometryEquiv.trans_assoc

∀ {𝕜 : Type u_1} {V : Type u_2} {V₂ : Type u_5} {V₃ : Type u_6} {V₄ : Type u_7} {P : Type u_10} {P₂ : Type u_11}
  {P₃ : Type u_12} {P₄ : Type u_13} [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] [inst_13 : SeminormedAddCommGroup V₄]
  [inst_14 : NormedSpace 𝕜 V₄] [inst_15 : PseudoMetricSpace P₄] [inst_16 : NormedAddTorsor V₄ P₄] (ePP₂ : P ≃ᵃⁱ[𝕜] P₂)
  (eP₂G : P₂ ≃ᵃⁱ[𝕜] P₃) (eGG' : P₃ ≃ᵃⁱ[𝕜] P₄), ePP₂.trans (eP₂G.trans eGG') = (ePP₂.trans eP₂G).trans eGG'

Defined in

Mathlib.Analysis.Normed.Affine.Isometry

Cited by

0 results in Mathlib

Foundations

Depth 50 from the axioms · uses propext, Quot.sound

Assumes

NormedFieldSeminormedAddCommGroupNormedSpacePseudoMetricSpaceNormedAddTorsorSeminormedAddCommGroupNormedSpacePseudoMetricSpaceNormedAddTorsorSeminormedAddCommGroupNormedSpacePseudoMetricSpaceNormedAddTorsorSeminormedAddCommGroupNormedSpacePseudoMetricSpaceNormedAddTorsor