-elim x. elim y.
-simplify.apply refl_eq.
-simplify.exact I.
-simplify.exact I.
-elim y. simplify.exact I.
-simplify.
-cut match (nat_compare n1 n) with
-[ LT \Rightarrow n1<n
-| EQ \Rightarrow n1=n
-| GT \Rightarrow n<n1] \to
-match (nat_compare n1 n) with
-[ LT \Rightarrow (S n1) \leq n
-| EQ \Rightarrow neg n = neg n1
-| GT \Rightarrow (S n) \leq n1].
-apply Hcut. apply nat_compare_to_Prop.
-elim (nat_compare n1 n).
-simplify.exact H.
-simplify.exact H.
-simplify.apply eq_f.apply sym_eq.exact H.
-simplify.exact I.
-elim y.simplify.exact I.
-simplify.exact I.
-simplify.
-cut match (nat_compare n n1) with
-[ LT \Rightarrow n<n1
-| EQ \Rightarrow n=n1
-| GT \Rightarrow n1<n] \to
-match (nat_compare n n1) with
-[ LT \Rightarrow (S n) \leq n1
-| EQ \Rightarrow pos n = pos n1
-| GT \Rightarrow (S n1) \leq n].
-apply Hcut. apply nat_compare_to_Prop.
-elim (nat_compare n n1).
-simplify.exact H.
-simplify.exact H.
-simplify.apply eq_f.exact H.
+elim x.
+ elim y.
+ simplify.apply refl_eq.
+ simplify.exact I.
+ simplify.exact I.
+ elim y.
+ simplify.exact I.
+ simplify.
+ cut (match (nat_compare n n1) with
+ [ LT \Rightarrow n<n1
+ | EQ \Rightarrow n=n1
+ | GT \Rightarrow n1<n] \to
+ match (nat_compare n n1) with
+ [ LT \Rightarrow (S n) \leq n1
+ | EQ \Rightarrow pos n = pos n1
+ | GT \Rightarrow (S n1) \leq n]).
+ apply Hcut.apply nat_compare_to_Prop.
+ elim (nat_compare n n1).
+ simplify.exact H.
+ simplify.apply eq_f.exact H.
+ simplify.exact H.
+ simplify.exact I.
+ elim y.
+ simplify.exact I.
+ simplify.exact I.
+ simplify.
+ cut (match (nat_compare n1 n) with
+ [ LT \Rightarrow n1<n
+ | EQ \Rightarrow n1=n
+ | GT \Rightarrow n<n1] \to
+ match (nat_compare n1 n) with
+ [ LT \Rightarrow (S n1) \leq n
+ | EQ \Rightarrow neg n = neg n1
+ | GT \Rightarrow (S n) \leq n1]).
+ apply Hcut. apply nat_compare_to_Prop.
+ elim (nat_compare n1 n).
+ simplify.exact H.
+ simplify.apply eq_f.apply sym_eq.exact H.
+ simplify.exact H.