(* This file was automatically generated: do not edit *********************)
-include "LambdaDelta-1/nf2/defs.ma".
+include "Basic-1/nf2/defs.ma".
-include "LambdaDelta-1/pr2/clen.ma".
+include "Basic-1/pr2/clen.ma".
-include "LambdaDelta-1/subst0/dec.ma".
+include "Basic-1/subst0/dec.ma".
-include "LambdaDelta-1/T/props.ma".
+include "Basic-1/T/props.ma".
theorem nf2_gen_lref:
\forall (c: C).(\forall (d: C).(\forall (u: T).(\forall (i: nat).((getl i c
Prop).(lift_gen_lref_false (S i) O i (le_O_n i) (le_n (plus O (S i))) u (H0
(lift (S i) O u) (pr2_delta c d u i H (TLRef i) (TLRef i) (pr0_refl (TLRef
i)) (lift (S i) O u) (subst0_lref u i))) P))))))).
+(* COMMENTS
+Initial nodes: 129
+END *)
theorem nf2_gen_abst:
\forall (c: C).(\forall (u: T).(\forall (t: T).((nf2 c (THead (Bind Abst) u
H_y))) in (let H2 \def (eq_ind_r T t2 (\lambda (t0: T).(pr2 (CHead c (Bind
Abst) u) t t0)) H0 t H1) in (eq_ind T t (\lambda (t0: T).(eq T t t0))
(refl_equal T t) t2 H1))))))))).
+(* COMMENTS
+Initial nodes: 353
+END *)
theorem nf2_gen_cast:
\forall (c: C).(\forall (u: T).(\forall (t: T).((nf2 c (THead (Flat Cast) u
\lambda (c: C).(\lambda (u: T).(\lambda (t: T).(\lambda (H: (nf2 c (THead
(Flat Cast) u t))).(\lambda (P: Prop).(thead_x_y_y (Flat Cast) u t (H t
(pr2_free c (THead (Flat Cast) u t) t (pr0_tau t t (pr0_refl t) u))) P))))).
+(* COMMENTS
+Initial nodes: 65
+END *)
theorem nf2_gen_beta:
\forall (c: C).(\forall (u: T).(\forall (v: T).(\forall (t: T).((nf2 c
Abbr) u t) (pr2_free c (THead (Flat Appl) u (THead (Bind Abst) v t)) (THead
(Bind Abbr) u t) (pr0_beta v u u (pr0_refl u) t t (pr0_refl t))))) in
(False_ind P H0))))))).
+(* COMMENTS
+Initial nodes: 183
+END *)
theorem nf2_gen_flat:
\forall (f: F).(\forall (c: C).(\forall (u: T).(\forall (t: T).((nf2 c
\Rightarrow t | (TLRef _) \Rightarrow t | (THead _ _ t0) \Rightarrow t0]))
(THead (Flat f) u t) (THead (Flat f) u t2) (H (THead (Flat f) u t2)
(pr2_head_2 c u t t2 (Flat f) (pr2_cflat c t t2 H0 f u)))) in H1)))))))).
+(* COMMENTS
+Initial nodes: 251
+END *)
theorem nf2_gen__nf2_gen_aux:
\forall (b: B).(\forall (x: T).(\forall (u: T).(\forall (d: nat).((eq T
t0)) (\lambda (t1: T).(eq T t1 t0)) H7 (THead (Bind b) (lift (S O) d t) (lift
(S O) (S d) t0)) (lift_bind b t t0 (S O) d)) in (H0 (lift (S O) d t) (S d) H8
P)))))) H3)) H2))))))))))) x)).
+(* COMMENTS
+Initial nodes: 935
+END *)
theorem nf2_gen_abbr:
\forall (c: C).(\forall (u: T).(\forall (t: T).((nf2 c (THead (Bind Abbr) u
(lift (S O) O x) H2) in (nf2_gen__nf2_gen_aux Abbr x u O (H3 x (pr2_free c
(THead (Bind Abbr) u (lift (S O) O x)) x (pr0_zeta Abbr not_abbr_abst x x
(pr0_refl x) u))) P))) H1))) H0))))))).
+(* COMMENTS
+Initial nodes: 511
+END *)
theorem nf2_gen_void:
\forall (c: C).(\forall (u: T).(\forall (t: T).((nf2 c (THead (Bind Void) u
Void t u O (H t (pr2_free c (THead (Bind Void) u (lift (S O) O t)) t
(pr0_zeta Void (sym_not_eq B Abst Void not_abst_void) t t (pr0_refl t) u)))
P))))).
+(* COMMENTS
+Initial nodes: 121
+END *)