Theorems · Theorem · convex and discrete geometry
Convexity.StdSimplex.ext
∀ {R : Type u} [inst : PartialOrder R] [inst_1 : Semiring R] {M : Type u_9} {f g : Convexity.StdSimplex R M},
f.weights = g.weights → f = gAlias of the forward direction of Convexity.StdSimplex.weights_inj.
- Defined in
- Mathlib.Geometry.Convex.ConvexSpace.Defs
- Cited by
- 14 results in Mathlib
- Foundations
- Depth 69 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- PartialOrderSemiring
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites6
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
- Convexity.StdSimplexstatement and proof · cited by 123
- Convexity.StdSimplex.weightsstatement · cited by 63
- Convexity.StdSimplex.weights_injproof · cited by 1
Cited by14
Results whose statement or proof uses this declaration.
- Convexity.iConvexComb_congrproof · cited by 10
- Convexity.StdSimplex.map_dupleproof · cited by 7
- Convexity.StdSimplex.map_constproof · cited by 4
- Convexity.convexCombPair_symmproof · cited by 3
- Convexity.StdSimplex.map_compproof · cited by 3
- Convexity.StdSimplex.map_idproof · cited by 2
- Convexity.iConvexComb_commproof · cited by 1
- Convexity.convexCombPair_convexCombPair_assoc_leftproof · cited by 1
- Convexity.StdSimplex.map_singleproof · cited by 1
- Convexity.IsConvexSet.imageproof · cited by 1
- Convexity.dist_convexCombPair_convexCombPairproof · cited by 1
- Convexity.StdSimplex.convexCombPair_restrict_restrict_complproof · cited by 1