(* This file was automatically generated: do not edit *********************)
-include "Basic-1/subst0/defs.ma".
+include "basic_1/subst0/defs.ma".
-include "Basic-1/lift/props.ma".
+include "basic_1/lift/props.ma".
-theorem dnf_dec2:
+lemma dnf_dec2:
\forall (t: T).(\forall (d: nat).(or (\forall (w: T).(ex T (\lambda (v:
T).(subst0 d w t (lift (S O) d v))))) (ex T (\lambda (v: T).(eq T t (lift (S
O) d v))))))
O) n v)))) (\lambda (w: T).(ex_intro T (\lambda (v: T).(subst0 n w (TLRef n)
(lift (S O) n v))) (lift n O w) (eq_ind_r T (lift (plus (S O) n) O w)
(\lambda (t0: T).(subst0 n w (TLRef n) t0)) (subst0_lref w n) (lift (S O) n
-(lift n O w)) (lift_free w n (S O) O n (le_n (plus O n)) (le_O_n n)))))) d
-H)) (\lambda (H: (lt d n)).(or_intror (\forall (w: T).(ex T (\lambda (v:
+(lift n O w)) (lift_free w n (S O) O n (le_plus_r O n) (le_O_n n)))))) d H))
+(\lambda (H: (lt d n)).(or_intror (\forall (w: T).(ex T (\lambda (v:
T).(subst0 d w (TLRef n) (lift (S O) d v))))) (ex T (\lambda (v: T).(eq T
(TLRef n) (lift (S O) d v)))) (ex_intro T (\lambda (v: T).(eq T (TLRef n)
(lift (S O) d v))) (TLRef (pred n)) (eq_ind_r T (TLRef n) (\lambda (t0:
(lift (S O) (s k d) x0)) t2)) (refl_equal T (THead k (lift (S O) d x) (lift
(S O) (s k d) x0))) (lift (S O) d (THead k x x0)) (lift_head k x x0 (S O)
d)))) t0 H3) t1 H6))) H5)) H4))))) H2)) H1))))))))) t).
-(* COMMENTS
-Initial nodes: 3549
-END *)
-theorem dnf_dec:
+lemma dnf_dec:
\forall (w: T).(\forall (t: T).(\forall (d: nat).(ex T (\lambda (v: T).(or
(subst0 d w t (lift (S O) d v)) (eq T t (lift (S O) d v)))))))
\def
(lift (S O) d v)))) x (or_intror (subst0 d w (lift (S O) d x) (lift (S O) d
x)) (eq T (lift (S O) d x) (lift (S O) d x)) (refl_equal T (lift (S O) d
x)))) t H1))) H0)) H))))).
-(* COMMENTS
-Initial nodes: 603
-END *)