-nat S (weight_map g (lift (S h) d t0)) (weight_map f (lift h d t0))
-(sym_equal nat (weight_map f (lift h d t0)) (weight_map g (lift (S h) d t0))
-(H h d f g H1 H2 H3))) m H5)) (\lambda (H5: (ex2 nat (\lambda (m0: nat).(eq
-nat m (S m0))) (\lambda (m: nat).(lt m d)))).(ex2_ind nat (\lambda (m0:
-nat).(eq nat m (S m0))) (\lambda (m0: nat).(lt m0 d)) (eq nat (wadd g (S
-(weight_map g (lift (S h) d t0))) m) (wadd f (S (weight_map f (lift h d t0)))
-m)) (\lambda (x: nat).(\lambda (H6: (eq nat m (S x))).(\lambda (H7: (lt x
-d)).(eq_ind_r nat (S x) (\lambda (n: nat).(eq nat (wadd g (S (weight_map g
-(lift (S h) d t0))) n) (wadd f (S (weight_map f (lift h d t0))) n))) (H1 x
-H7) m H6)))) H5)) (lt_gen_xS m d H4)))) H2 (\lambda (m: nat).(\lambda (H4:
-(le (S d) m)).(ex2_ind nat (\lambda (n: nat).(eq nat m (S n))) (\lambda (n:
-nat).(le d n)) (eq nat (g m) (wadd f (S (weight_map f (lift h d t0))) m))
-(\lambda (x: nat).(\lambda (H5: (eq nat m (S x))).(\lambda (H6: (le d
-x)).(eq_ind_r nat (S x) (\lambda (n: nat).(eq nat (g n) (wadd f (S
-(weight_map f (lift h d t0))) n))) (H3 x H6) m H5)))) (le_gen_S d m H4)))))))
-(f_equal nat nat S (plus (weight_map f (lift h d t0)) (weight_map (wadd f O)
-(lift h (S d) t1))) (plus (weight_map g (lift (S h) d t0)) (weight_map (wadd
-g O) (lift (S h) (S d) t1))) (f_equal2 nat nat nat plus (weight_map f (lift h
-d t0)) (weight_map g (lift (S h) d t0)) (weight_map (wadd f O) (lift h (S d)
-t1)) (weight_map (wadd g O) (lift (S h) (S d) t1)) (H h d f g H1 H2 H3) (H0 h
-(S d) (wadd f O) (wadd g O) (\lambda (m: nat).(\lambda (H4: (lt m (S
+nat S (weight_map g (lift (S h) d t0)) (weight_map f (lift h d t0)) (sym_eq
+nat (weight_map f (lift h d t0)) (weight_map g (lift (S h) d t0)) (H h d f g
+H1 H2 H3))) m H5)) (\lambda (H5: (ex2 nat (\lambda (m0: nat).(eq nat m (S
+m0))) (\lambda (m0: nat).(lt m0 d)))).(ex2_ind nat (\lambda (m0: nat).(eq nat
+m (S m0))) (\lambda (m0: nat).(lt m0 d)) (eq nat (wadd g (S (weight_map g
+(lift (S h) d t0))) m) (wadd f (S (weight_map f (lift h d t0))) m)) (\lambda
+(x: nat).(\lambda (H6: (eq nat m (S x))).(\lambda (H7: (lt x d)).(eq_ind_r
+nat (S x) (\lambda (n: nat).(eq nat (wadd g (S (weight_map g (lift (S h) d
+t0))) n) (wadd f (S (weight_map f (lift h d t0))) n))) (H1 x H7) m H6))))
+H5)) (lt_gen_xS m d H4)))) H2 (\lambda (m: nat).(\lambda (H4: (le (S d)
+m)).(ex2_ind nat (\lambda (n: nat).(eq nat m (S n))) (\lambda (n: nat).(le d
+n)) (eq nat (g m) (wadd f (S (weight_map f (lift h d t0))) m)) (\lambda (x:
+nat).(\lambda (H5: (eq nat m (S x))).(\lambda (H6: (le d x)).(eq_ind_r nat (S
+x) (\lambda (n: nat).(eq nat (g n) (wadd f (S (weight_map f (lift h d t0)))
+n))) (H3 x H6) m H5)))) (le_gen_S d m H4))))))) (f_equal nat nat S (plus
+(weight_map f (lift h d t0)) (weight_map (wadd f O) (lift h (S d) t1))) (plus
+(weight_map g (lift (S h) d t0)) (weight_map (wadd g O) (lift (S h) (S d)
+t1))) (f_equal2 nat nat nat plus (weight_map f (lift h d t0)) (weight_map g
+(lift (S h) d t0)) (weight_map (wadd f O) (lift h (S d) t1)) (weight_map
+(wadd g O) (lift (S h) (S d) t1)) (H h d f g H1 H2 H3) (H0 h (S d) (wadd f O)
+(wadd g O) (\lambda (m: nat).(\lambda (H4: (lt m (S d))).(or_ind (eq nat m O)
+(ex2 nat (\lambda (m0: nat).(eq nat m (S m0))) (\lambda (m0: nat).(lt m0 d)))
+(eq nat (wadd g O m) (wadd f O m)) (\lambda (H5: (eq nat m O)).(eq_ind_r nat
+O (\lambda (n: nat).(eq nat (wadd g O n) (wadd f O n))) (refl_equal nat O) m
+H5)) (\lambda (H5: (ex2 nat (\lambda (m0: nat).(eq nat m (S m0))) (\lambda
+(m0: nat).(lt m0 d)))).(ex2_ind nat (\lambda (m0: nat).(eq nat m (S m0)))
+(\lambda (m0: nat).(lt m0 d)) (eq nat (wadd g O m) (wadd f O m)) (\lambda (x:
+nat).(\lambda (H6: (eq nat m (S x))).(\lambda (H7: (lt x d)).(eq_ind_r nat (S
+x) (\lambda (n: nat).(eq nat (wadd g O n) (wadd f O n))) (H1 x H7) m H6))))
+H5)) (lt_gen_xS m d H4)))) H2 (\lambda (m: nat).(\lambda (H4: (le (S d)
+m)).(ex2_ind nat (\lambda (n: nat).(eq nat m (S n))) (\lambda (n: nat).(le d
+n)) (eq nat (g m) (wadd f O m)) (\lambda (x: nat).(\lambda (H5: (eq nat m (S
+x))).(\lambda (H6: (le d x)).(eq_ind_r nat (S x) (\lambda (n: nat).(eq nat (g
+n) (wadd f O n))) (H3 x H6) m H5)))) (le_gen_S d m H4))))))) (f_equal nat nat
+S (plus (weight_map f (lift h d t0)) (weight_map (wadd f O) (lift h (S d)
+t1))) (plus (weight_map g (lift (S h) d t0)) (weight_map (wadd g O) (lift (S
+h) (S d) t1))) (f_equal2 nat nat nat plus (weight_map f (lift h d t0))
+(weight_map g (lift (S h) d t0)) (weight_map (wadd f O) (lift h (S d) t1))
+(weight_map (wadd g O) (lift (S h) (S d) t1)) (H h d f g H1 H2 H3) (H0 h (S
+d) (wadd f O) (wadd g O) (\lambda (m: nat).(\lambda (H4: (lt m (S