Theorems · Theorem · convex and discrete geometry

Convexity.StdSimplex.map_duple

∀ {R : Type u} [inst : PartialOrder R] [inst_1 : Semiring R] {M : Type u_9} {N : Type u_10}
  [inst_2 : IsStrictOrderedRing R] {s t : R} (hs : 0 ≤ s) (ht : 0 ≤ t) (h : s + t = 1) (x y : M) (f : M → N),
  Convexity.StdSimplex.map f (Convexity.StdSimplex.duple x y hs ht h) = Convexity.StdSimplex.duple (f x) (f y) hs ht h

Defined in

Mathlib.Geometry.Convex.ConvexSpace.Defs

Cited by

7 results in Mathlib

Foundations

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

Assumes

PartialOrderSemiringIsStrictOrderedRing