include "pr3/fwd.ma".
-include "iso/fwd.ma".
+include "iso/props.ma".
theorem nf2_iso_appls_lref:
\forall (c: C).(\forall (i: nat).((nf2 c (TLRef i)) \to (\forall (vs:
(\lambda (u: T).(\lambda (H0: (pr3 c (TLRef i) u)).(let H_y \def
(nf2_pr3_unfold c (TLRef i) u H0 H) in (let H1 \def (eq_ind_r T u (\lambda
(t: T).(pr3 c (TLRef i) t)) H0 (TLRef i) H_y) in (eq_ind T (TLRef i) (\lambda
-(t: T).(iso (TLRef i) t)) (iso_lref i i) u H_y))))) (\lambda (t: T).(\lambda
-(t0: TList).(\lambda (H0: ((\forall (u: T).((pr3 c (THeads (Flat Appl) t0
-(TLRef i)) u) \to (iso (THeads (Flat Appl) t0 (TLRef i)) u))))).(\lambda (u:
-T).(\lambda (H1: (pr3 c (THead (Flat Appl) t (THeads (Flat Appl) t0 (TLRef
-i))) u)).(let H2 \def (pr3_gen_appl c t (THeads (Flat Appl) t0 (TLRef i)) u
-H1) in (or3_ind (ex3_2 T T (\lambda (u2: T).(\lambda (t2: T).(eq T u (THead
-(Flat Appl) u2 t2)))) (\lambda (u2: T).(\lambda (_: T).(pr3 c t u2)))
-(\lambda (_: T).(\lambda (t2: T).(pr3 c (THeads (Flat Appl) t0 (TLRef i))
-t2)))) (ex4_4 T T T T (\lambda (_: T).(\lambda (_: T).(\lambda (u2:
-T).(\lambda (t2: T).(pr3 c (THead (Bind Abbr) u2 t2) u))))) (\lambda (_:
+(t: T).(iso (TLRef i) t)) (iso_refl (TLRef i)) u H_y))))) (\lambda (t:
+T).(\lambda (t0: TList).(\lambda (H0: ((\forall (u: T).((pr3 c (THeads (Flat
+Appl) t0 (TLRef i)) u) \to (iso (THeads (Flat Appl) t0 (TLRef i))
+u))))).(\lambda (u: T).(\lambda (H1: (pr3 c (THead (Flat Appl) t (THeads
+(Flat Appl) t0 (TLRef i))) u)).(let H2 \def (pr3_gen_appl c t (THeads (Flat
+Appl) t0 (TLRef i)) u H1) in (or3_ind (ex3_2 T T (\lambda (u2: T).(\lambda
+(t2: T).(eq T u (THead (Flat Appl) u2 t2)))) (\lambda (u2: T).(\lambda (_:
+T).(pr3 c t u2))) (\lambda (_: T).(\lambda (t2: T).(pr3 c (THeads (Flat Appl)
+t0 (TLRef i)) t2)))) (ex4_4 T T T T (\lambda (_: T).(\lambda (_: T).(\lambda
+(u2: T).(\lambda (t2: T).(pr3 c (THead (Bind Abbr) u2 t2) u))))) (\lambda (_:
T).(\lambda (_: T).(\lambda (u2: T).(\lambda (_: T).(pr3 c t u2))))) (\lambda
(y1: T).(\lambda (z1: T).(\lambda (_: T).(\lambda (_: T).(pr3 c (THeads (Flat
Appl) t0 (TLRef i)) (THead (Bind Abst) y1 z1)))))) (\lambda (_: T).(\lambda
T).(\lambda (x1: T).(\lambda (H4: (eq T u (THead (Flat Appl) x0
x1))).(\lambda (_: (pr3 c t x0)).(\lambda (_: (pr3 c (THeads (Flat Appl) t0
(TLRef i)) x1)).(eq_ind_r T (THead (Flat Appl) x0 x1) (\lambda (t1: T).(iso
-(THead (Flat Appl) t (THeads (Flat Appl) t0 (TLRef i))) t1)) (iso_head (Flat
-Appl) t x0 (THeads (Flat Appl) t0 (TLRef i)) x1) u H4)))))) H3)) (\lambda
+(THead (Flat Appl) t (THeads (Flat Appl) t0 (TLRef i))) t1)) (iso_head t x0
+(THeads (Flat Appl) t0 (TLRef i)) x1 (Flat Appl)) u H4)))))) H3)) (\lambda
(H3: (ex4_4 T T T T (\lambda (_: T).(\lambda (_: T).(\lambda (u2: T).(\lambda
(t2: T).(pr3 c (THead (Bind Abbr) u2 t2) u))))) (\lambda (_: T).(\lambda (_:
T).(\lambda (u2: T).(\lambda (_: T).(pr3 c t u2))))) (\lambda (y1: