Theorems · Theorem · convex and discrete geometry
Convexity.sConvexComb_sConvexComb
∀ {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] (f : Convexity.StdSimplex R (Convexity.StdSimplex R M)),
Convexity.sConvexComb (Convexity.sConvexComb f) =
Convexity.sConvexComb (Convexity.StdSimplex.map Convexity.sConvexComb f)- Defined in
- Mathlib.Geometry.Convex.ConvexSpace.Defs
- Cited by
- 4 results in Mathlib
- Foundations
- Depth 80 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites8
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
- Convexity.ConvexSpacestatement and proof · cited by 176
- Convexity.StdSimplexstatement and proof · cited by 123
- Convexity.ConvexSpace.sConvexCombstatement · cited by 59
- Convexity.StdSimplex.mapstatement · cited by 43
- Convexity.ConvexSpace.assocproof · cited by 1
Cited by4
Results whose statement or proof uses this declaration.
- Convexity.iConvexComb_assoc'proof · cited by 2
- Convexity.sConvexComb_convexCombPairproof · cited by 1
- Convexity.iConvexComb_assoc''proof · cited by 1
- Convexity.iConvexComb_assocproof · cited by 0