Theorems · Theorem · convex and discrete geometry
Convexity.StdSimplex.weights_map
∀ {R : Type u} [inst : PartialOrder R] [inst_1 : Semiring R] [inst_2 : IsStrictOrderedRing R] {M : Type v} {N : Type w}
(g : M → N) (f : Convexity.StdSimplex R M), (Convexity.StdSimplex.map g f).weights = Finsupp.mapDomain g f.weights- Defined in
- Mathlib.Geometry.Convex.ConvexSpace.Defs
- Cited by
- 18 results in Mathlib
- Foundations
- Depth 76 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
- Finsuppstatement · cited by 5,255
- IsStrictOrderedRingstatement and proof · cited by 2,490
- Finsupp.mapDomainstatement · cited by 168
- Convexity.StdSimplexstatement and proof · cited by 123
- Convexity.StdSimplex.weightsstatement and proof · cited by 63
- Convexity.StdSimplex.mapstatement and proof · cited by 43
Cited by18
Results whose statement or proof uses this declaration.
- Convexity.iConvexComb_congrproof · cited by 10
- Convexity.iConvexComb_eq_sumproof · cited by 9
- Convexity.StdSimplex.map_dupleproof · cited by 7
- Convexity.dist_iConvexComb_leproof · cited by 5
- Convexity.StdSimplex.map_constproof · cited by 4
- Convexity.StdSimplex.map_compproof · cited by 3
- Convexity.StdSimplex.map_idproof · cited by 2
- Convexity.IsAffineMap.addproof · cited by 2
- Convexity.IsAffineMap.negproof · cited by 2
- Convexity.IsConvexSet.iConvexComb_memproof · cited by 1
- Convexity.StdSimplex.map_singleproof · cited by 1
- Convexity.IsConvexSet.imageproof · cited by 1