-(H3: (lt (weight_map f0 (lift (S i) O v)) (g i))).(lt_le_S (plus (weight_map
-f0 u0) (weight_map f0 t2)) (S (plus (weight_map g u0) (weight_map g t1)))
-(le_lt_n_Sm (plus (weight_map f0 u0) (weight_map f0 t2)) (plus (weight_map g
-u0) (weight_map g t1)) (plus_le_compat (weight_map f0 u0) (weight_map g u0)
-(weight_map f0 t2) (weight_map g t1) (weight_le u0 f0 g H2) (H1 f0 g H2
-H3)))))))))))))))) k)) (\lambda (v: T).(\lambda (u1: T).(\lambda (u2:
-T).(\lambda (i: nat).(\lambda (_: (subst0 i v u1 u2)).(\lambda (H1: ((\forall
-(f: ((nat \to nat))).(\forall (g: ((nat \to nat))).(((\forall (m: nat).(le (f
-m) (g m)))) \to ((lt (weight_map f (lift (S i) O v)) (g i)) \to (le
-(weight_map f u2) (weight_map g u1)))))))).(\lambda (k: K).(K_ind (\lambda
-(k0: K).(\forall (t1: T).(\forall (t2: T).((subst0 (s k0 i) v t1 t2) \to
-(((\forall (f: ((nat \to nat))).(\forall (g: ((nat \to nat))).(((\forall (m:
-nat).(le (f m) (g m)))) \to ((lt (weight_map f (lift (S (s k0 i)) O v)) (g (s
-k0 i))) \to (le (weight_map f t2) (weight_map g t1))))))) \to (\forall (f:
-((nat \to nat))).(\forall (g: ((nat \to nat))).(((\forall (m: nat).(le (f m)
-(g m)))) \to ((lt (weight_map f (lift (S i) O v)) (g i)) \to (le (weight_map
-f (THead k0 u2 t2)) (weight_map g (THead k0 u1 t1)))))))))))) (\lambda (b:
-B).(B_ind (\lambda (b0: B).(\forall (t1: T).(\forall (t2: T).((subst0 (s
-(Bind b0) i) v t1 t2) \to (((\forall (f: ((nat \to nat))).(\forall (g: ((nat
+(H3: (lt (weight_map f0 (lift (S i) O v)) (g i))).(le_n_S (plus (weight_map
+f0 u0) (weight_map f0 t2)) (plus (weight_map g u0) (weight_map g t1))
+(plus_le_compat (weight_map f0 u0) (weight_map g u0) (weight_map f0 t2)
+(weight_map g t1) (weight_le u0 f0 g H2) (H1 f0 g H2 H3))))))))))))))) k))
+(\lambda (v: T).(\lambda (u1: T).(\lambda (u2: T).(\lambda (i: nat).(\lambda
+(_: (subst0 i v u1 u2)).(\lambda (H1: ((\forall (f: ((nat \to nat))).(\forall
+(g: ((nat \to nat))).(((\forall (m: nat).(le (f m) (g m)))) \to ((lt
+(weight_map f (lift (S i) O v)) (g i)) \to (le (weight_map f u2) (weight_map
+g u1)))))))).(\lambda (k: K).(K_ind (\lambda (k0: K).(\forall (t1:
+T).(\forall (t2: T).((subst0 (s k0 i) v t1 t2) \to (((\forall (f: ((nat \to
+nat))).(\forall (g: ((nat \to nat))).(((\forall (m: nat).(le (f m) (g m))))
+\to ((lt (weight_map f (lift (S (s k0 i)) O v)) (g (s k0 i))) \to (le
+(weight_map f t2) (weight_map g t1))))))) \to (\forall (f: ((nat \to
+nat))).(\forall (g: ((nat \to nat))).(((\forall (m: nat).(le (f m) (g m))))
+\to ((lt (weight_map f (lift (S i) O v)) (g i)) \to (le (weight_map f (THead
+k0 u2 t2)) (weight_map g (THead k0 u1 t1)))))))))))) (\lambda (b: B).(B_ind
+(\lambda (b0: B).(\forall (t1: T).(\forall (t2: T).((subst0 (s (Bind b0) i) v
+t1 t2) \to (((\forall (f: ((nat \to nat))).(\forall (g: ((nat \to
+nat))).(((\forall (m: nat).(le (f m) (g m)))) \to ((lt (weight_map f (lift (S
+(s (Bind b0) i)) O v)) (g (s (Bind b0) i))) \to (le (weight_map f t2)
+(weight_map g t1))))))) \to (\forall (f: ((nat \to nat))).(\forall (g: ((nat