Theorems · Theorem · convex and discrete geometry

Convexity.convexCombPair_same

∀ {R : Type u_1} {M : Type u_3} [inst : PartialOrder R] [inst_1 : Semiring R] [inst_2 : IsStrictOrderedRing R]
  [inst_3 : Convexity.ConvexSpace R M] {s t : R} (hs : 0 ≤ s) (ht : 0 ≤ t) (h : s + t = 1) {x : M},
  Convexity.convexCombPair s t hs ht h x x = x

A convex combination of a point with itself is that point.

Defined in

Mathlib.Geometry.Convex.ConvexSpace.Defs

Cited by

2 results in Mathlib

Foundations

Depth 74 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

PartialOrderSemiringIsStrictOrderedRingConvexity.ConvexSpace