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}.

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).