Theorems · Theorem · convex and discrete geometry
Convexity.subtypeVal_submodule_sConvexComb
∀ {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) (w : Convexity.StdSimplex R ↥S),
↑(Convexity.sConvexComb w) = Convexity.iConvexComb w Subtype.val- Cited by
- 0 results in Mathlib
- Foundations
- Depth 85 from the axioms · uses propext, Classical.choice, Quot.sound
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Cites13
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Modulestatement and proof · cited by 20,661
- Semiringstatement and proof · cited by 13,802
- AddCommMonoidstatement and proof · cited by 12,281
- PartialOrderstatement and proof · cited by 6,410
- IsStrictOrderedRingstatement and proof · cited by 2,490
- SetLikestatement and proof · cited by 1,084
- AddSubmonoidClassstatement and proof · cited by 346
- Convexity.ConvexSpacestatement and proof · cited by 176
- Convexity.StdSimplexstatement and proof · cited by 123
- SMulMemClassstatement and proof · cited by 77
- Convexity.ConvexSpace.sConvexCombstatement · cited by 59
- Convexity.iConvexCombstatement · cited by 51
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