-set "baseuri" "cic:/matita/TPTP/BOO075-1".
+
inductive eq (A:Type) (x:A) : A \to Prop \def refl_eq : eq A x x.
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.
qed.
default "equality"
- cic:/matita/TPTP/BOO075-1/eq.ind
- cic:/matita/TPTP/BOO075-1/sym_eq.con
- 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_f.con
- cic:/matita/TPTP/BOO075-1/eq_f1.con.
+ cic:/matita/tests/paramodulation/BOO075-1/eq.ind
+ cic:/matita/tests/paramodulation/BOO075-1/sym_eq.con
+ cic:/matita/tests/paramodulation/BOO075-1/trans_eq.con
+ cic:/matita/tests/paramodulation/BOO075-1/eq_ind.con
+ cic:/matita/tests/paramodulation/BOO075-1/eq_elim_r.con
+ cic:/matita/tests/paramodulation/BOO075-1/eq_rec.con
+ cic:/matita/tests/paramodulation/BOO075-1/eq_elim_r'.con
+ cic:/matita/tests/paramodulation/BOO075-1/eq_rect.con
+ cic:/matita/tests/paramodulation/BOO075-1/eq_elim_r''.con
+ cic:/matita/tests/paramodulation/BOO075-1/eq_f.con
+ cic:/matita/tests/paramodulation/BOO075-1/eq_f1.con.
theorem eq_f: \forall A,B:Type.\forall f:A\to B.
\forall x,y:A. eq A x y \to eq B (f x) (f y).
inductive ex (A:Type) (P:A \to Prop) : Prop \def
ex_intro: \forall x:A. P x \to ex A P.
interpretation "exists" 'exists \eta.x =
- (cic:/matita/TPTP/BOO075-1/ex.ind#xpointer(1/1) _ x).
+ (cic:/matita/tests/paramodulation/BOO075-1/ex.ind#xpointer(1/1) _ x).
notation < "hvbox(\exists ident i opt (: ty) break . p)"
right associative with precedence 20
\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
+(* -------------------------------------------------------------------------- *)