Theorems · Theorem · convex and discrete geometry

mk_mem_convexHull_prod

∀ {R : Type u_1} {E : Type u_3} {F : Type u_4} [inst : Field R] [inst_1 : AddCommGroup E] [inst_2 : AddCommGroup F]
  [inst_3 : Module R E] [inst_4 : Module R F] {s : Set E} [inst_5 : LinearOrder R] [IsStrictOrderedRing R] {t : Set F}
  {x : E} {y : F}, x ∈ (convexHull R) s → y ∈ (convexHull R) t → (x, y) ∈ (convexHull R) (s ×ˢ t)

Defined in

Mathlib.Analysis.Convex.Combination

Cited by

1 results in Mathlib

Foundations

Depth 79 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

FieldAddCommGroupAddCommGroupModuleModuleLinearOrderIsStrictOrderedRing