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Theorems · Theorem · convex and discrete geometry

Convexity.IsConvexSet.empty

∀ {R : Type u_3} {X : Type u_5} [inst : Semiring R] [inst_1 : PartialOrder R] [inst_2 : IsStrictOrderedRing R]
  [inst_3 : Convexity.ConvexSpace R X], Convexity.IsConvexSet R ∅
Defined in
Mathlib.Geometry.Convex.Set
Cited by
2 results in Mathlib
Foundations
Depth 65 from the axioms · uses propext, Classical.choice, Quot.sound
Assumes
SemiringPartialOrderIsStrictOrderedRingConvexity.ConvexSpace
Mathlib docsSourceLoogleLeanSearch

Around this declaration

Dashed lines are statement dependencies; solid lines are citations in proofs.

Convexity.convexHull_empty · cited by 1Convexity.convexHull_emptyConvexity.convexHull_eq_empty · cited by 0Convexity.convexHull_eq_e…Set · cited by 53352SetSemiring · cited by 13802SemiringPartialOrder · cited by 6410PartialOrderIsStrictOrderedRing · cited by 2490IsStrictOrderedRingConvexity.ConvexSpace · cited by 176Convexity.ConvexSpaceConvexity.StdSimplex · cited by 123Convexity.StdSimplexConvexity.ConvexSpace.sConvexComb · cited by 59ConvexSpace.sConvexCombConvexity.IsConvexSet · cited by 35Convexity.IsConvexSetIsConvexSet.emptyCITED BYCITES

Cites8

Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.

Cited by2

Results whose statement or proof uses this declaration.