Theorems · Theorem · convex and discrete geometry

Convexity.convexCombPair_iConvexComb_iConvexComb

∀ {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) {J₁ : Type u₁} {J₂ : Type u₂}
  (g₁ : Convexity.StdSimplex R J₁) (g₂ : Convexity.StdSimplex R J₂) (m₁ : J₁ → M) (m₂ : J₂ → M),
  Convexity.convexCombPair s t hs ht h (Convexity.iConvexComb g₁ m₁) (Convexity.iConvexComb g₂ m₂) =
    Convexity.sConvexComb
      (Convexity.convexCombPair s t hs ht h (Convexity.StdSimplex.map m₁ g₁) (Convexity.StdSimplex.map m₂ g₂))

Flattening with the outer combination specialized to convexCombPair.

Defined in

Mathlib.Geometry.Convex.ConvexSpace.Defs

Cited by

2 results in Mathlib

Foundations

Depth 82 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

PartialOrderSemiringIsStrictOrderedRingConvexity.ConvexSpace