open Classical

theorem ex : if (fun x => x + 1) = (fun x => x + 2) then False else True := by
  have (fun x => x + 1) ≠ (fun x => x + 2) by
    intro h
    have 1 = 2 from congrFun h 0
    contradiction
  rw ifNeg this
  exact True.intro

def tst (x : Nat) : Bool :=
  if 1 < 2 then true else false