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Theorems · Theorem · convex and discrete geometry

Convexity.convexComboPair_one

Deprecated since 2026-05-15Use Convexity.convexCombPair_one instead.

∀ {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] {x y : M}, Convexity.convexCombPair 1 0 ⋯ ⋯ ⋯ x y = x

Alias of Convexity.convexCombPair_one. A binary convex combination with weight 1 on the first point returns the first point.

Defined in
Mathlib.Geometry.Convex.ConvexSpace.Defs
Cited by
0 results in Mathlib
Foundations
Depth 75 from the axioms · uses propext, Classical.choice, Quot.sound
Assumes
PartialOrderSemiringIsStrictOrderedRingConvexity.ConvexSpace
Mathlib docsSourceLoogleLeanSearch

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Semiring · cited by 13802SemiringPartialOrder · cited by 6410PartialOrderIsStrictOrderedRing · cited by 2490IsStrictOrderedRingConvexity.ConvexSpace · cited by 176Convexity.ConvexSpaceConvexity.convexCombPair · cited by 52Convexity.convexCombPairConvexity.convexCombPair_one · cited by 3Convexity.convexCombPair_…Convexity.convexComboPair_oneCITED BYCITES

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