Theorems · Theorem · convex and discrete geometry

quasilinearOn_iff_monotoneOn_or_antitoneOn

∀ {𝕜 : Type u_1} {β : Type u_3} [inst : Field 𝕜] [inst_1 : LinearOrder 𝕜] [IsStrictOrderedRing 𝕜] {s : Set 𝕜}
  {f : 𝕜 → β} [inst_3 : LinearOrder β], Convex 𝕜 s → (QuasilinearOn 𝕜 s f ↔ MonotoneOn f s ∨ AntitoneOn f s)

Defined in

Mathlib.Analysis.Convex.Quasiconvex

Cited by

0 results in Mathlib

Foundations

Depth 65 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

FieldLinearOrderIsStrictOrderedRingLinearOrder