-- Generated by the EML-lang Lean backend
-- Source module: sine_oscillator
-- Source file:   /home/monogate/monogate/forge/examples/sine_oscillator.eml
-- Verified fns:  oscillate

import MachLib.EML
import MachLib.Trig
import MachLib.Forge
import MachLib.Linarith
import MachLib.FixedPoint
import MachLib.SignTactic

open MachLib
open MachLib.Real

-- ── oscillate ──

noncomputable def oscillate (amplitude : Real) (omega : Real) (t : Real) : Real :=
  (amplitude * (Real.sin (omega * t)))

theorem sine_oscillator_amplitude_bound (amplitude : Real) (omega : Real) (t : Real)
    (h1 : (amplitude >= (0 : Real)))
    (h2 : (amplitude <= (1 : Real)))
    (h3 : (omega >= (0 : Real)))
    (h4 : (omega <= (10000.0 : Real)))
    (h5 : (t >= (0 : Real))) :
    ((abs (oscillate amplitude omega t)) <= amplitude) := by
  unfold oscillate
  first
  | (apply lo_le_clamp <;> (first | assumption | mach_positivity))
  | apply clamp_le_hi
  | mach_positivity
  | mach_sign
  | rfl
  | sorry  -- out of reach; left for the prover