(** [negate_condition cond] returns a condition that is logically
  equivalent to the negation of [cond]. *)

Definition negate_condition (cond: condition): condition :=
  match cond with
  | Ccomp c => Ccomp(negate_comparison c)
  | Ccompu c => Ccompu(negate_comparison c)
  | Ccompimm c n => Ccompimm (negate_comparison c) n
  | Ccompuimm c n => Ccompuimm (negate_comparison c) n
  | Ccompl c => Ccompl(negate_comparison c)
  | Ccomplu c => Ccomplu(negate_comparison c)
  | Ccomplimm c n => Ccomplimm (negate_comparison c) n
  | Ccompluimm c n => Ccompluimm (negate_comparison c) n
  | Ccompf c => Cnotcompf c
  | Cnotcompf c => Ccompf c
  | Ccompfs c => Cnotcompfs c
  | Cnotcompfs c => Ccompfs c
  end.

(* Specifications: *)
Lemma eval_negate_condition: forall cond vl m, eval_condition (negate_condition cond) vl m = option_map negb (eval_condition cond vl m).