simplify. intros.
generalize in match H1.
rewrite < H2; rewrite < H3.intro.
- rewrite > H4.auto new library.
+ rewrite > H4.autobatch library.
qed.
focus 633. clearbody k3.
exact
(eq_ind A b (\lambda x:A.(eq A x b)) (refl_equal A b) (add (multiply a b) b) (eq_ind A (multiply b n1) (\lambda x:A.(eq A x (add (multiply a b) b))) (eq_ind_r A (add a n1) (\lambda x:A.(eq A (multiply b x) (add (multiply a b) b))) (eq_ind_r A (multiply n1 b) (\lambda x:A.(eq A (multiply b (add a n1)) (add (multiply a b) x))) (H5 b a n1) b (eq_ind A (multiply b n1) (\lambda x:A.(eq A b (multiply n1 x))) (eq_ind A (multiply b n1) (\lambda x:A.(eq A x (multiply n1 (multiply b n1)))) (eq_ind_r A (add b b) (\lambda x:A.(eq A (multiply b n1) (multiply n1 x))) (eq_ind A (add n1 n1) (\lambda x:A.(eq A (multiply b x) (multiply n1 (add b b)))) (eq_ind A (add n1 n1) (\lambda x:A.(eq A (multiply b (add n1 n1)) (multiply x (add b b)))) (eq_ind_r A (add (multiply b (add n1 n1)) (multiply b (add n1 n1))) (\lambda x:A.(eq A (multiply b (add n1 n1)) x)) (eq_ind_r A (add (multiply n1 b) (multiply n1 b)) (\lambda x:A.(eq A (multiply b (add n1 n1)) (add (multiply b (add n1 n1)) x))) (eq_ind_r A (add (multiply n1 b) (multiply n1 b)) (\lambda x:A.(eq A x (add (multiply b (add n1 n1)) (add (multiply n1 b) (multiply n1 b))))) (eq_ind_r A (add (multiply n1 b) (multiply n1 b)) (\lambda x:A.(eq A (add (multiply n1 b) (multiply n1 b)) (add x (add (multiply n1 b) (multiply n1 b))))) (eq_ind A (multiply (add (multiply n1 b) (multiply n1 b)) n1) (\lambda x:A.(eq A x (add (add (multiply n1 b) (multiply n1 b)) (add (multiply n1 b) (multiply n1 b))))) (H7 (multiply n1 b)) (add (multiply n1 b) (multiply n1 b)) (H8 (multiply n1 b))) (multiply b (add n1 n1)) (H5 b n1 n1)) (multiply b (add n1 n1)) (H5 b n1 n1)) (multiply b (add n1 n1)) (H5 b n1 n1)) (multiply (add n1 n1) (add b b)) (H5 (add n1 n1) b b)) n1 (eq_ind A (multiply (add n1 n1) n1) (\lambda x:A.(eq A x n1)) (H6 n1 n1) (add n1 n1) (H8 n1))) n1 (eq_ind A (multiply (add n1 n1) n1) (\lambda x:A.(eq A x n1)) (H6 n1 n1) (add n1 n1) (H8 n1))) (multiply b n1) (eq_ind_r A (multiply n1 (add b b)) (\lambda x:A.(eq A x (add b b))) (eq_ind A (multiply (add b b) n1) (\lambda x:A.(eq A (multiply n1 (add b b)) x)) (eq_ind A (add n1 n1) (\lambda x:A.(eq A (multiply n1 (add b b)) (multiply (add b b) x))) (eq_ind_r A (add (multiply n1 (add b b)) (multiply n1 (add b b))) (\lambda x:A.(eq A (multiply n1 (add b b)) x)) (eq_ind_r A (add (multiply b n1) (multiply b n1)) (\lambda x:A.(eq A (multiply n1 (add b b)) (add (multiply n1 (add b b)) x))) (eq_ind_r A (add (multiply b n1) (multiply b n1)) (\lambda x:A.(eq A x (add (multiply n1 (add b b)) (add (multiply b n1) (multiply b n1))))) (eq_ind_r A (add (multiply b n1) (multiply b n1)) (\lambda x:A.(eq A (add (multiply b n1) (multiply b n1)) (add x (add (multiply b n1) (multiply b n1))))) (eq_ind A (multiply (add (multiply b n1) (multiply b n1)) n1) (\lambda x:A.(eq A x (add (add (multiply b n1) (multiply b n1)) (add (multiply b n1) (multiply b n1))))) (H7 (multiply b n1)) (add (multiply b n1) (multiply b n1)) (H8 (multiply b n1))) (multiply n1 (add b b)) (H5 n1 b b)) (multiply n1 (add b b)) (H5 n1 b b)) (multiply n1 (add b b)) (H5 n1 b b)) (multiply (add b b) (add n1 n1)) (H5 (add b b) n1 n1)) n1 (eq_ind A (multiply (add n1 n1) n1) (\lambda x:A.(eq A x n1)) (H6 n1 n1) (add n1 n1) (H8 n1))) (add b b) (H8 b)) (multiply b n1) (eq_ind A (add n1 n1) (\lambda x:A.(eq A (multiply b x) (multiply n1 (add b b)))) (eq_ind A (add n1 n1) (\lambda x:A.(eq A (multiply b (add n1 n1)) (multiply x (add b b)))) (eq_ind_r A (add (multiply b (add n1 n1)) (multiply b (add n1 n1))) (\lambda x:A.(eq A (multiply b (add n1 n1)) x)) (eq_ind_r A (add (multiply n1 b) (multiply n1 b)) (\lambda x:A.(eq A (multiply b (add n1 n1)) (add (multiply b (add n1 n1)) x))) (eq_ind_r A (add (multiply n1 b) (multiply n1 b)) (\lambda x:A.(eq A x (add (multiply b (add n1 n1)) (add (multiply n1 b) (multiply n1 b))))) (eq_ind_r A (add (multiply n1 b) (multiply n1 b)) (\lambda x:A.(eq A (add (multiply n1 b) (multiply n1 b)) (add x (add (multiply n1 b) (multiply n1 b))))) (eq_ind A (multiply (add (multiply n1 b) (multiply n1 b)) n1) (\lambda x:A.(eq A x (add (add (multiply n1 b) (multiply n1 b)) (add (multiply n1 b) (multiply n1 b))))) (H7 (multiply n1 b)) (add (multiply n1 b) (multiply n1 b)) (H8 (multiply n1 b))) (multiply b (add n1 n1)) (H5 b n1 n1)) (multiply b (add n1 n1)) (H5 b n1 n1)) (multiply b (add n1 n1)) (H5 b n1 n1)) (multiply (add n1 n1) (add b b)) (H5 (add n1 n1) b b)) n1 (eq_ind A (multiply (add n1 n1) n1) (\lambda x:A.(eq A x n1)) (H6 n1 n1) (add n1 n1) (H8 n1))) n1 (eq_ind A (multiply (add n1 n1) n1) (\lambda x:A.(eq A x n1)) (H6 n1 n1) (add n1 n1) (H8 n1))))) b ?) b ?)) n1 ?) b ?)).
-auto new.
-auto new.
-auto new.
-auto new.
+autobatch.
+autobatch.
+autobatch.
+autobatch.
unfocus.
-auto new.
+autobatch.
unfocus.
-auto new.
+autobatch.
unfocus.
-auto new.
+autobatch.
unfocus.
-auto new.
+autobatch.
qed.
simplify. intros.
generalize in match H1.
rewrite < H2; rewrite < H3.intro.
- rewrite > H4.auto new library.
+ rewrite > H4.autobatch library.
qed.
theorem t1: \forall x,y. sum x y O \to x = y.
inversion s.
intros.simplify.
intros.
-rewrite > H. rewrite < H2. auto new library.
+rewrite > H. rewrite < H2. autobatch library.
qed.
rewrite < (plus_n_O x).
reflexivity.
reflexivity.
- auto new library.
+ autobatch library.
qed.
(* This test tests "replace in match t" where t contains some metavariables *)
theorem b:\forall p:nat. p * 0=0.
intro.
-auto new library.
+autobatch library.
qed.