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Theorems · Theorem · convex and discrete geometry

inter_extremePoints_subset_extremePoints_of_subset

∀ {𝕜 : Type u_1} {E : Type u_2} [inst : Semiring 𝕜] [inst_1 : PartialOrder 𝕜] [inst_2 : AddCommMonoid E]
  [inst_3 : SMul 𝕜 E] {A B : Set E}, B ⊆ A → B ∩ Set.extremePoints 𝕜 A ⊆ Set.extremePoints 𝕜 B
Defined in
Mathlib.Analysis.Convex.Extreme
Cited by
2 results in Mathlib
Foundations
Depth 15 from the axioms · uses no axioms
Assumes
SemiringPartialOrderAddCommMonoidSMul
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Around this declaration

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

IsExtreme.extremePoints_eq · cited by 0IsExtreme.extremePoints_eqConvex.convexIndependent_extremePoints · cited by 0Convex.convexIndependent_…Set · cited by 53352SetSemiring · cited by 13802SemiringAddCommMonoid · cited by 12281AddCommMonoidPartialOrder · cited by 6410PartialOrderopenSegment · cited by 102openSegmentSet.extremePoints · cited by 43Set.extremePointsinter_extremePoints_subset_ex…CITED BYCITES

Cites6

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Cited by2

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