Theorems · Theorem · convex and discrete geometry

Convexity.IsAffineMap.add

∀ {R : Type u_2} {M : Type u_3} {N : Type u_4} [inst : Semiring R] [inst_1 : PartialOrder R]
  [inst_2 : IsStrictOrderedRing R] [inst_3 : AddCommMonoid M] [inst_4 : Module R M] [inst_5 : AddCommMonoid N]
  [inst_6 : Module R N] {f g : M → N} [inst_7 : Convexity.ConvexSpace R M] [Convexity.IsModuleConvexSpace R M]
  [inst_9 : Convexity.ConvexSpace R N] [Convexity.IsModuleConvexSpace R N],
  Convexity.IsAffineMap R f → Convexity.IsAffineMap R g → Convexity.IsAffineMap R (f + g)

Defined in

Mathlib.Geometry.Convex.ConvexSpace.Module

Cited by

2 results in Mathlib

Foundations

Depth 80 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

SemiringPartialOrderIsStrictOrderedRingAddCommMonoidModuleAddCommMonoidModuleConvexity.ConvexSpaceConvexity.IsModuleConvexSpaceConvexity.ConvexSpaceConvexity.IsModuleConvexSpace