Theorems · Theorem · convex and discrete geometry

Convexity.IsAffineMap.neg

∀ {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 : AddCommGroup M] [inst_4 : Module R M] [inst_5 : AddCommGroup N]
  [inst_6 : Module R N] [inst_7 : Convexity.ConvexSpace R M] [Convexity.IsModuleConvexSpace R M]
  [inst_9 : Convexity.ConvexSpace R N] [Convexity.IsModuleConvexSpace R N] {f : M → N},
  Convexity.IsAffineMap R f → Convexity.IsAffineMap R (-f)

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

SemiringPartialOrderIsStrictOrderedRingAddCommGroupModuleAddCommGroupModuleConvexity.ConvexSpaceConvexity.IsModuleConvexSpaceConvexity.ConvexSpaceConvexity.IsModuleConvexSpace