Theorems · Theorem · convex and discrete geometry

Convexity.convexCombPair_convexCombPair_assoc_left

∀ {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) {s' t' : R} (hs' : 0 ≤ s')
  (ht' : 0 ≤ t') (h' : s' + t' = 1) {s'' t'' : R} (hs'' : 0 ≤ s'') (ht'' : 0 ≤ t'') (h'' : s'' + t'' = 1),
  t * s'' = s * t' * t'' →
    ∀ (m₁ m₂ m₃ : M),
      Convexity.convexCombPair s t hs ht h (Convexity.convexCombPair s' t' hs' ht' h' m₁ m₂) m₃ =
        Convexity.convexCombPair (s * s') (s * t' + t) ⋯ ⋯ ⋯ m₁ (Convexity.convexCombPair s'' t'' hs'' ht'' h'' m₂ m₃)

Defined in

Mathlib.Geometry.Convex.ConvexSpace.Defs

Cited by

1 results in Mathlib

Foundations

Depth 85 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

PartialOrderSemiringIsStrictOrderedRingConvexity.ConvexSpace