Theorems · Theorem · convex and discrete geometry

Convexity.subtypeVal_submodule_convexCombPair

∀ {F : Type u_1} {R : Type u_2} {M : Type u_3} [inst : Semiring R] [inst_1 : PartialOrder R]
  [inst_2 : IsStrictOrderedRing R] [inst_3 : AddCommMonoid M] [inst_4 : Module R M] [inst_5 : SetLike F M]
  [inst_6 : AddSubmonoidClass F M] [inst_7 : SMulMemClass F R M] [inst_8 : Convexity.ConvexSpace R M]
  [inst_9 : Convexity.IsModuleConvexSpace R M] (S : F) (a b : R) (ha : 0 ≤ a) (hb : 0 ≤ b) (hab : a + b = 1) (x y : ↥S),
  ↑(Convexity.convexCombPair a b ha hb hab x y) = Convexity.convexCombPair a b ha hb hab ↑x ↑y

Defined in

Mathlib.Geometry.Convex.ConvexSpace.Module

Cited by

0 results in Mathlib

Foundations

Depth 86 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

SemiringPartialOrderIsStrictOrderedRingAddCommMonoidModuleSetLikeAddSubmonoidClassSMulMemClassConvexity.ConvexSpaceConvexity.IsModuleConvexSpace