(eq_ind_r nat (plus (trans hds0 i) h) (\lambda (n: nat).(eq T (lift (S n) O
(lift1 (ptrans hds0 i) t)) (lift (S (plus (trans hds0 i) h)) O (lift1 (ptrans
hds0 i) t)))) (refl_equal T (lift (S (plus (trans hds0 i) h)) O (lift1
-(ptrans hds0 i) t))) (plus h (trans hds0 i)) (plus_comm h (trans hds0 i)))
+(ptrans hds0 i) t))) (plus h (trans hds0 i)) (plus_sym h (trans hds0 i)))
(plus h (S (trans hds0 i))) (plus_n_Sm h (trans hds0 i))) (lift h d (lift (S
(trans hds0 i)) O (lift1 (ptrans hds0 i) t))) (lift_free (lift1 (ptrans hds0
i) t) (S (trans hds0 i)) h O d (eq_ind nat (S (plus O (trans hds0 i)))
(\lambda (n: nat).(le d n)) (eq_ind_r nat (plus (trans hds0 i) O) (\lambda
(n: nat).(le d (S n))) (le_S d (plus (trans hds0 i) O) (le_plus_trans d
(trans hds0 i) O (bge_le d (trans hds0 i) H0))) (plus O (trans hds0 i))
-(plus_comm O (trans hds0 i))) (plus O (S (trans hds0 i))) (plus_n_Sm O (trans
+(plus_sym O (trans hds0 i))) (plus O (S (trans hds0 i))) (plus_n_Sm O (trans
hds0 i))) (le_O_n d)))) x_x))) (lift1 hds0 (lift (S i) O t)) (H i t))))))))
hds).