End Not_Rules.
Section Other_Rules.

(* Specifications: *)
Lemma impRefl : forall (T : System) (f : Formula), SysPrf T (impH f f).
Lemma impTrans :
forall (T : System) (f g h : Formula),
SysPrf T (impH f g) -> SysPrf T (impH g h) -> SysPrf T (impH f h).
Lemma orSym :
forall (T : System) (f g : Formula),
SysPrf T (orH f g) -> SysPrf T (orH g f).
Lemma andSym :
forall (T : System) (f g : Formula),
SysPrf T (andH f g) -> SysPrf T (andH g f).
Lemma iffRefl : forall (T : System) (f : Formula), SysPrf T (iffH f f).
Lemma iffSym :
forall (T : System) (f g : Formula),
SysPrf T (iffH f g) -> SysPrf T (iffH g f).
Lemma iffTrans :
forall (T : System) (f g h : Formula),
SysPrf T (iffH f g) -> SysPrf T (iffH g h) -> SysPrf T (iffH f h).