Definition st_ok (st : STt) (interp: positive -> COINCpoint) :=
forall t, STmem t st = true -> app wd (interp_CP t interp).
Context {COT : Coinc_theory AR COP}.

(* Specifications: *)
Lemma identify_varieties_ok : forall ss st interp,
ss_ok ss interp -> st_ok st interp ->
ss_ok (identify_varieties ss st) interp.
Lemma test_coinc_ok : forall ss st interp cp,
ss_ok ss interp -> st_ok st interp ->
test_coinc ss st cp = true ->
app coinc (interp_CP cp interp).
Lemma ss_ok_empty : forall interp,
ss_ok SS.empty interp.
Lemma st_ok_empty : forall interp,
st_ok STempty interp.