Theorems · Theorem · convex and discrete geometry
Convexity.convexCombPair_zero
∀ {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 = yA binary convex combination with weight 0 on the first point returns the second point.
- Defined in
- Mathlib.Geometry.Convex.ConvexSpace.Defs
- Cited by
- 2 results in Mathlib
- Foundations
- Depth 74 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites11
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Semiringstatement and proof · cited by 13,802
- PartialOrderstatement and proof · cited by 6,410
- IsStrictOrderedRingstatement and proof · cited by 2,490
- zero_addproof · cited by 2,366
- Finsupp.singleproof · cited by 943
- Convexity.ConvexSpacestatement and proof · cited by 176
- Finsupp.single_zeroproof · cited by 63
- Convexity.ConvexSpace.sConvexCombproof · cited by 59
- Convexity.convexCombPairstatement · cited by 52
- Convexity.ConvexSpace.sConvexComb_singleproof · cited by 9
- Convexity.StdSimplex.mk.congr_simpproof · cited by 5
Cited by2
Results whose statement or proof uses this declaration.
- Convexity.continuous_convexCombPair_of_isBoundedproof · cited by 1
- Convexity.convexComboPair_zeroproof · cited by 0