Theorems · Theorem · general topology

Convexity.dist_convexCombPair_left

∀ {X : Type u_2} [inst : Convexity.ConvexSpace ℝ X] [inst_1 : MetricSpace X] [Convexity.IsConvexDist X] {s t : ℝ}
  (hs : 0 ≤ s) (ht : 0 ≤ t) (h : s + t = 1) (x y : X), dist (Convexity.convexCombPair s t hs ht h x y) x = t * dist x y

Defined in

Mathlib.Analysis.Convex.MetricSpace

Cited by

4 results in Mathlib

Foundations

Depth 109 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

Convexity.ConvexSpaceMetricSpaceConvexity.IsConvexDist