FormalConjecturesForMathlib.Order.Unimodular

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Copyright 2026 The Formal Conjectures Authors.

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module


public import Mathlib.Data.Real.Basic
public import Mathlib.Order.Interval.Set.Defs
public import Mathlib.Order.Monotone.Basic

@[expose] public section

Unimodular sequences

A sequence is unimodular on (a, ∞) if it increases up to some point and decreases after it.

f is unimodular on (a, ∞) if it increases until some point M > a and decreases thereafter.

def UnimodularOn (f : ℕ → ℝ) (a : ℕ) : Prop :=
  ∃ M > a, MonotoneOn f (Set.Ioc a M) ∧ AntitoneOn f (Set.Ici M)