(* This file was automatically generated: do not edit *********************)
-include "LambdaDelta-1/C/defs.ma".
+include "Basic-1/C/defs.ma".
-include "LambdaDelta-1/T/props.ma".
+include "Basic-1/T/props.ma".
theorem clt_cong:
\forall (c: C).(\forall (d: C).((clt c d) \to (\forall (k: K).(\forall (t:
\lambda (c: C).(\lambda (d: C).(\lambda (H: (lt (cweight c) (cweight
d))).(\lambda (_: K).(\lambda (t: T).(lt_reg_r (cweight c) (cweight d)
(tweight t) H))))).
+(* COMMENTS
+Initial nodes: 33
+END *)
theorem clt_head:
\forall (k: K).(\forall (c: C).(\forall (u: T).(clt c (CHead c k u))))
c) O) (\lambda (n: nat).(lt n (plus (cweight c) (tweight u))))
(le_lt_plus_plus (cweight c) (cweight c) O (tweight u) (le_n (cweight c))
(tweight_lt u)) (cweight c) (plus_n_O (cweight c))))).
+(* COMMENTS
+Initial nodes: 69
+END *)
theorem clt_wf__q_ind:
\forall (P: ((C \to Prop))).(((\forall (n: nat).((\lambda (P0: ((C \to
Prop))).(\lambda (H: ((\forall (n: nat).(\forall (c: C).((eq nat (cweight c)
n) \to (P c)))))).(\lambda (c: C).(H (cweight c) c (refl_equal nat (cweight
c)))))).
+(* COMMENTS
+Initial nodes: 61
+END *)
theorem clt_wf_ind:
\forall (P: ((C \to Prop))).(((\forall (c: C).(((\forall (d: C).((clt d c)
c1)))))) H0 (cweight c0) H1) in (H c0 (\lambda (d: C).(\lambda (H3: (lt
(cweight d) (cweight c0))).(H2 (cweight d) H3 d (refl_equal nat (cweight
d))))))))))))) c)))).
+(* COMMENTS
+Initial nodes: 179
+END *)
theorem chead_ctail:
\forall (c: C).(\forall (t: T).(\forall (k: K).(ex_3 K C T (\lambda (h:
C).(\lambda (u: T).(eq C (CHead (CTail x0 x2 x1) k0 t0) (CTail h u d))))) x0
(CHead x1 k0 t0) x2 (refl_equal C (CHead (CTail x0 x2 x1) k0 t0))) (CHead c0
k t) H1))))) H0))))))))) c).
+(* COMMENTS
+Initial nodes: 395
+END *)
theorem clt_thead:
\forall (k: K).(\forall (u: T).(\forall (c: C).(clt c (CTail k u c))))
c0 (CTail k u c0))) (\lambda (n: nat).(clt_head k (CSort n) u)) (\lambda (c0:
C).(\lambda (H: (clt c0 (CTail k u c0))).(\lambda (k0: K).(\lambda (t:
T).(clt_cong c0 (CTail k u c0) H k0 t))))) c))).
+(* COMMENTS
+Initial nodes: 71
+END *)
theorem c_tail_ind:
\forall (P: ((C \to Prop))).(((\forall (n: nat).(P (CSort n)))) \to
(eq_ind C (CHead c1 k t) (\lambda (c2: C).(\forall (d: C).((clt d c2) \to (P
d)))) H2 (CTail x0 x2 x1) H4) in (H0 x1 (H5 x1 (clt_thead x0 x2 x1)) x0 x2))
(CHead c1 k t) H4))))) H3)))))))) c0)) c)))).
+(* COMMENTS
+Initial nodes: 295
+END *)