Theorems · Theorem · convex and discrete geometry
Convexity.convexComboPair_zero
Deprecated since 2026-05-15Use Convexity.convexCombPair_zero 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 0 1 ⋯ ⋯ ⋯ x y = yAlias of Convexity.convexCombPair_zero.
A binary convex combination with weight 0 on the first point returns the second 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
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Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Semiringstatement · cited by 13,802
- PartialOrderstatement · cited by 6,410
- IsStrictOrderedRingstatement · cited by 2,490
- Convexity.ConvexSpacestatement · cited by 176
- Convexity.convexCombPairstatement · cited by 52
- Convexity.convexCombPair_zeroproof · cited by 2
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