Theorems · Theorem · general topology
Convexity.dist_sConvexComb_right_le
∀ {X : Type u_2} [inst : Convexity.ConvexSpace ℝ X] [inst_1 : MetricSpace X] [Convexity.IsConvexDist X] (x : X)
(f : Convexity.StdSimplex ℝ X), dist x (Convexity.sConvexComb f) ≤ Convexity.iConvexComb f (dist x)- Defined in
- Mathlib.Analysis.Convex.MetricSpace
- Cited by
- 0 results in Mathlib
- Foundations
- Depth 108 from the axioms · uses propext, Classical.choice, Quot.sound
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Cites14
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- DFunLike.coeproof · cited by 62,936
- Realstatement and proof · cited by 25,697
- MetricSpacestatement and proof · cited by 1,684
- Dist.diststatement and proof · cited by 1,539
- Convexity.ConvexSpacestatement and proof · cited by 176
- Convexity.StdSimplexstatement and proof · cited by 123
- Convexity.StdSimplex.weightsproof · cited by 63
- Convexity.ConvexSpace.sConvexCombstatement and proof · cited by 59
- Convexity.iConvexCombstatement · cited by 51
- Convexity.IsConvexDiststatement and proof · cited by 18
- Convexity.iConvexComb_congrproof · cited by 10
- Convexity.iConvexComb_eq_sumproof · cited by 9
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