Definition check_normalised_formulas : list NFormula -> Psatz -> bool :=
fun l cm =>
match eval_Psatz l cm with
| None => false
| Some f => check_inconsistent f
end.

Lemma checker_nf_sound :
forall (l : list NFormula) (cm : Psatz),
check_normalised_formulas l cm = true ->
forall env : PolEnv, make_impl (eval_nformula env) l False.