Theorems · Theorem · convex and discrete geometry

Convexity.IsAffineMap.map_convexCombPair

∀ {R : Type u_1} {M : Type u_3} {N : Type u_4} [inst : PartialOrder R] [inst_1 : Semiring R]
  [inst_2 : IsStrictOrderedRing R] [inst_3 : Convexity.ConvexSpace R M] [inst_4 : Convexity.ConvexSpace R N]
  {f : M → N},
  Convexity.IsAffineMap R f →
    ∀ {s t : R} (hs : 0 ≤ s) (ht : 0 ≤ t) (h : s + t = 1) (x y : M),
      f (Convexity.convexCombPair s t hs ht h x y) = Convexity.convexCombPair s t hs ht h (f x) (f y)

Defined in

Mathlib.Geometry.Convex.ConvexSpace.Defs

Cited by

8 results in Mathlib

Foundations

Depth 78 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

PartialOrderSemiringIsStrictOrderedRingConvexity.ConvexSpaceConvexity.ConvexSpace