Theorems · Theorem · convex and discrete geometry

Sbtw.dist_lt_max_dist

∀ {V : Type u_1} {P : Type u_2} [inst : NormedAddCommGroup V] [inst_1 : NormedSpace ℝ V] [StrictConvexSpace ℝ V]
  [inst_3 : PseudoMetricSpace P] [inst_4 : NormedAddTorsor V P] (p : P) {p₁ p₂ p₃ : P},
  Sbtw ℝ p₁ p₂ p₃ → dist p₂ p < max (dist p₁ p) (dist p₃ p)

Defined in

Mathlib.Analysis.Convex.StrictConvexBetween

Cited by

2 results in Mathlib

Foundations

Depth 166 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

NormedAddCommGroupNormedSpaceStrictConvexSpacePseudoMetricSpaceNormedAddTorsor