Theorems · Theorem · convex and discrete geometry

Convexity.iConvexComb_congr

∀ {R : Type u_1} {M : Type u_3} {I : Type u_6} [inst : PartialOrder R] [inst_1 : Semiring R]
  [inst_2 : IsStrictOrderedRing R] [inst_3 : Convexity.ConvexSpace R M] {w : Convexity.StdSimplex R I} {f g : I → M},
  (∀ (i : I), w.weights i ≠ 0 → f i = g i) → Convexity.iConvexComb w f = Convexity.iConvexComb w g

Defined in

Mathlib.Geometry.Convex.ConvexSpace.Defs

Cited by

10 results in Mathlib

Foundations

Depth 77 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

PartialOrderSemiringIsStrictOrderedRingConvexity.ConvexSpace