Theorems · Theorem · geometry

AffineIsometry.map_eq_iff

∀ {𝕜 : Type u_1} {V₁' : Type u_4} {V₂ : Type u_5} {P₁' : Type u_9} {P₂ : Type u_11} [inst : NormedField 𝕜]
  [inst_1 : SeminormedAddCommGroup V₁'] [inst_2 : NormedSpace 𝕜 V₁'] [inst_3 : MetricSpace P₁']
  [inst_4 : NormedAddTorsor V₁' P₁'] [inst_5 : SeminormedAddCommGroup V₂] [inst_6 : NormedSpace 𝕜 V₂]
  [inst_7 : PseudoMetricSpace P₂] [inst_8 : NormedAddTorsor V₂ P₂] (f₁ : P₁' →ᵃⁱ[𝕜] P₂) {x y : P₁'}, f₁ x = f₁ y ↔ x = y

Defined in

Mathlib.Analysis.Normed.Affine.Isometry

Cited by

1 results in Mathlib

Foundations

Depth 160 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

NormedFieldSeminormedAddCommGroupNormedSpaceMetricSpaceNormedAddTorsorSeminormedAddCommGroupNormedSpacePseudoMetricSpaceNormedAddTorsor