intros. elim (sym_eq ? ? ? H1).assumption.
qed.
+theorem eq_elim_r':
+ \forall A:Type.\forall x:A. \forall P: A \to Set.
+ P x \to \forall y:A. eq A y x \to P y.
+intros. elim (sym_eq ? ? ? H).assumption.
+qed.
+
+theorem eq_elim_r'':
+ \forall A:Type.\forall x:A. \forall P: A \to Type.
+ P x \to \forall y:A. eq A y x \to P y.
+intros. elim (sym_eq ? ? ? H).assumption.
+qed.
+
theorem trans_eq :
\forall A:Type.\forall x,y,z:A. eq A x y \to eq A y z \to eq A x z.
intros.elim H1.assumption.
cic:/matita/TPTP/BOO075-1/trans_eq.con
cic:/matita/TPTP/BOO075-1/eq_ind.con
cic:/matita/TPTP/BOO075-1/eq_elim_r.con
+ cic:/matita/TPTP/BOO075-1/eq_rec.con
+ cic:/matita/TPTP/BOO075-1/eq_elim_r'.con
+ cic:/matita/TPTP/BOO075-1/eq_rect.con
+ cic:/matita/TPTP/BOO075-1/eq_elim_r''.con
cic:/matita/TPTP/BOO075-1/eq_f.con
cic:/matita/TPTP/BOO075-1/eq_f1.con.
\forall H0:\forall A:Univ.\forall B:Univ.\forall C:Univ.eq Univ (nand (nand A (nand (nand B A) A)) (nand B (nand C A))) B.eq Univ (nand (nand a a) (nand b a)) a
.
intros.
-auto paramodulation timeout=600.
+autobatch paramodulation timeout=600;
try assumption.
print proofterm.
qed.
-(* -------------------------------------------------------------------------- *)
\ No newline at end of file
+(* -------------------------------------------------------------------------- *)