Theorems · Theorem · convex and discrete geometry

PointedCone.minTensorProduct_mono

∀ {R : Type u_1} [inst : CommRing R] [inst_1 : LinearOrder R] [inst_2 : IsStrictOrderedRing R] {G : Type u_2}
  [inst_3 : AddCommGroup G] [inst_4 : Module R G] {H : Type u_3} [inst_5 : AddCommGroup H] [inst_6 : Module R H]
  {C₁ C₁' : PointedCone R G} {C₂ C₂' : PointedCone R H},
  C₁ ≤ C₁' → C₂ ≤ C₂' → C₁.minTensorProduct C₂ ≤ C₁'.minTensorProduct C₂'

minTensorProduct is monotone.

Defined in

Mathlib.Geometry.Convex.Cone.TensorProduct

Cited by

0 results in Mathlib

Foundations

Depth 57 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

CommRingLinearOrderIsStrictOrderedRingAddCommGroupModuleAddCommGroupModule