(* This file was automatically generated: do not edit *********************)
-set "baseuri" "cic:/matita/LAMBDA-TYPES/LambdaDelta-1/lift1/props".
+include "LambdaDelta-1/lift/props.ma".
-include "lift1/defs.ma".
-
-include "lift/props.ma".
-
-include "drop1/defs.ma".
+include "LambdaDelta-1/drop1/defs.ma".
theorem lift1_lift1:
\forall (is1: PList).(\forall (is2: PList).(\forall (t: T).(eq T (lift1 is1
t))))) (\lambda (is2: PList).(\lambda (t: T).(refl_equal T (lift1 is2 t))))
(\lambda (n: nat).(\lambda (n0: nat).(\lambda (p: PList).(\lambda (H:
((\forall (is2: PList).(\forall (t: T).(eq T (lift1 p (lift1 is2 t)) (lift1
-(papp p is2) t)))))).(\lambda (is2: PList).(\lambda (t: T).(sym_eq T (lift n
-n0 (lift1 (papp p is2) t)) (lift n n0 (lift1 p (lift1 is2 t))) (sym_eq T
-(lift n n0 (lift1 p (lift1 is2 t))) (lift n n0 (lift1 (papp p is2) t))
-(sym_eq T (lift n n0 (lift1 (papp p is2) t)) (lift n n0 (lift1 p (lift1 is2
-t))) (f_equal3 nat nat T T lift n n n0 n0 (lift1 (papp p is2) t) (lift1 p
-(lift1 is2 t)) (refl_equal nat n) (refl_equal nat n0) (sym_eq T (lift1 p
-(lift1 is2 t)) (lift1 (papp p is2) t) (H is2 t)))))))))))) is1).
+(papp p is2) t)))))).(\lambda (is2: PList).(\lambda (t: T).(f_equal3 nat nat
+T T lift n n n0 n0 (lift1 p (lift1 is2 t)) (lift1 (papp p is2) t) (refl_equal
+nat n) (refl_equal nat n0) (H is2 t)))))))) is1).
theorem lift1_xhg:
\forall (hds: PList).(\forall (t: T).(eq T (lift1 (Ss hds) (lift (S O) O t))
(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).