Theorems · Theorem · geometry

AffineIsometryEquiv.coe_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] (e₁ : P ≃ᵃⁱ[𝕜] P₂)
  (e₂ : P₂ ≃ᵃⁱ[𝕜] P₃), ⇑(e₁.trans e₂) = ⇑e₂ ∘ ⇑e₁

Defined in

Mathlib.Analysis.Normed.Affine.Isometry

Cited by

0 results in Mathlib

Foundations

Depth 51 from the axioms · uses propext, Quot.sound

Assumes

NormedFieldSeminormedAddCommGroupNormedSpacePseudoMetricSpaceNormedAddTorsorSeminormedAddCommGroupNormedSpacePseudoMetricSpaceNormedAddTorsorSeminormedAddCommGroupNormedSpacePseudoMetricSpaceNormedAddTorsor