Theorems · Theorem · convex and discrete geometry

Convexity.IsConvexSet.preimage

∀ {R : Type u_3} {X : Type u_5} {Y : Type u_6} [inst : Semiring R] [inst_1 : PartialOrder R]
  [inst_2 : IsStrictOrderedRing R] [inst_3 : Convexity.ConvexSpace R X] [inst_4 : Convexity.ConvexSpace R Y] {f : X → Y}
  {s : Set Y}, Convexity.IsAffineMap R f → Convexity.IsConvexSet R s → Convexity.IsConvexSet R (f ⁻¹' s)

Defined in

Mathlib.Geometry.Convex.Set

Cited by

1 results in Mathlib

Foundations

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

Assumes

SemiringPartialOrderIsStrictOrderedRingConvexity.ConvexSpaceConvexity.ConvexSpace