Definition semax'  := HORec semax_.Definition semax vars (G: funspecs) (P: assert) (k: control) : Prop :=
       typecheck vars k = true /\ forall n,  semax' (SemaxArg vars (fun s => P s && funassert G) k) n.Definition semax_func (G: funspecs) (p: program) (G': funspecs) :=
    match_specs p G' /\
    forall n, believe_all semax' G p G' n.

Lemma semax_func_cons: forall fs id f vars P (G G': funspecs), inlist id (map (@fst adr (list var * control)) fs) = false -> list_nodups vars = true -> length vars = length (fst P) -> semax vars G (fun s => call P (map s vars)) f -> semax_func G fs G' -> semax_func G ((id, (vars,f))::fs) ((id, P) :: G').