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Theorems · Theorem · convex and discrete geometry

StarConvex.prod

∀ {𝕜 : Type u_1} {E : Type u_2} {F : Type u_3} [inst : Semiring 𝕜] [inst_1 : PartialOrder 𝕜] [inst_2 : AddCommMonoid E]
  [inst_3 : AddCommMonoid F] [inst_4 : SMul 𝕜 E] [inst_5 : SMul 𝕜 F] {x : E} {y : F} {s : Set E} {t : Set F},
  StarConvex 𝕜 x s → StarConvex 𝕜 y t → StarConvex 𝕜 (x, y) (s ×ˢ t)
Defined in
Mathlib.Analysis.Convex.Star
Cited by
2 results in Mathlib
Foundations
Depth 14 from the axioms · uses propext, Quot.sound
Assumes
SemiringPartialOrderAddCommMonoidAddCommMonoidSMulSMul
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Around this declaration

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

Convex.prod · cited by 4Convex.prodStarConvex.add · cited by 1StarConvex.addSet · cited by 53352SetSemiring · cited by 13802SemiringAddCommMonoid · cited by 12281AddCommMonoidPartialOrder · cited by 6410PartialOrderSProd.sprod · cited by 1750SProd.sprodStarConvex · cited by 62StarConvexStarConvex.prodCITED BYCITES

Cites6

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.