Section Not_Rules.

(* Specifications: *)
Lemma absurd1 :
forall (T : System) (f : Formula),
SysPrf T (impH f (notH f)) -> SysPrf T (notH f).
Lemma nImp :
forall (T : System) (f g : Formula),
SysPrf T (andH f (notH g)) -> SysPrf T (notH (impH f g)).
Lemma nOr :
forall (T : System) (f g : Formula),
SysPrf T (andH (notH f) (notH g)) -> SysPrf T (notH (orH f g)).
Lemma nAnd :
forall (T : System) (f g : Formula),
SysPrf T (orH (notH f) (notH g)) -> SysPrf T (notH (andH f g)).
Lemma nForall :
forall (T : System) (f : Formula) (v : nat),
SysPrf T (existH v (notH f)) -> SysPrf T (notH (forallH v f)).
Lemma nExist :
forall (T : System) (f : Formula) (v : nat),
SysPrf T (forallH v (notH f)) -> SysPrf T (notH (existH v f)).