Theorems · Theorem · convex and discrete geometry

Convex.translate_preimage_right

∀ {𝕜 : Type u_1} {E : Type u_2} [inst : Semiring 𝕜] [inst_1 : PartialOrder 𝕜] [inst_2 : AddCommMonoid E]
  [inst_3 : Module 𝕜 E] {s : Set E}, Convex 𝕜 s → ∀ (z : E), Convex 𝕜 ((fun x => z + x) ⁻¹' s)

The translation of a convex set is also convex.

Defined in

Mathlib.Analysis.Convex.Basic

Cited by

3 results in Mathlib

Foundations

Depth 14 from the axioms · uses propext

Assumes

SemiringPartialOrderAddCommMonoidModule