-elim x.elim y.
-left.reflexivity.
-right.apply not_eq_OZ_neg.
-right.apply not_eq_OZ_pos.
-elim y.right.intro.
-apply not_eq_OZ_neg n ?.apply sym_eq.assumption.
-elim (decidable_eq_nat n n1:(Or (n=n1) ((n=n1) \to False))).
-left.apply eq_f.assumption.
-right.intro.apply H.apply injective_neg.assumption.
-right.intro.apply not_eq_pos_neg n1 n ?.apply sym_eq.assumption.
-elim y.right.intro.
-apply not_eq_OZ_pos n ?.apply sym_eq.assumption.
-right.apply not_eq_pos_neg.
-elim (decidable_eq_nat n n1:(Or (n=n1) ((n=n1) \to False))).
-left.apply eq_f.assumption.
-right.intro.apply H.apply injective_pos.assumption.
+elim x.
+(* goal: x=OZ *)
+ elim y.
+ (* goal: x=OZ y=OZ *)
+ left.reflexivity.
+ (* goal: x=OZ 2=2 *)
+ right.apply not_eq_OZ_pos.
+ (* goal: x=OZ 2=3 *)
+ right.apply not_eq_OZ_neg.
+(* goal: x=pos *)
+ elim y.
+ (* goal: x=pos y=OZ *)
+ right.intro.
+ apply not_eq_OZ_pos n. symmetry. assumption.
+ (* goal: x=pos y=pos *)
+ elim (decidable_eq_nat n n1:((n=n1) \lor ((n=n1) \to False))).
+ left.apply eq_f.assumption.
+ right.intros [H_inj].apply H. injection H_inj. assumption.
+ (* goal: x=pos y=neg *)
+ right.intro.apply not_eq_pos_neg n n1. assumption.
+(* goal: x=neg *)
+ elim y.
+ (* goal: x=neg y=OZ *)
+ right.intro.
+ apply not_eq_OZ_neg n. symmetry. assumption.
+ (* goal: x=neg y=pos *)
+ right. intro. apply not_eq_pos_neg n1 n. symmetry. assumption.
+ (* goal: x=neg y=neg *)
+ elim (decidable_eq_nat n n1:((n=n1) \lor ((n=n1) \to False))).
+ left.apply eq_f.assumption.
+ right.intro.apply H.apply injective_neg.assumption.