Theorems · Theorem · geometry

signedDist_lineMap_lineMap

∀ {V : Type u_1} {P : Type u_2} [inst : NormedAddCommGroup V] [inst_1 : InnerProductSpace ℝ V] [inst_2 : MetricSpace P]
  [inst_3 : NormedAddTorsor V P] (v : V) (p q : P) (c₁ c₂ : ℝ),
  ((signedDist v) ((AffineMap.lineMap p q) c₁)) ((AffineMap.lineMap p q) c₂) = (c₂ - c₁) * ((signedDist v) p) q

Defined in

Mathlib.Geometry.Euclidean.SignedDist

Cited by

4 results in Mathlib

Foundations

Depth 180 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

NormedAddCommGroupInnerProductSpaceMetricSpaceNormedAddTorsor