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_assign: forall x y c vars G P,
expcheck vars y = true ->
semax (vs_add x vars) G P c ->
semax vars G (fun s => |> subst x (eval y s) P s) (Do x := y ; c).