include "basic_1/C/defs.ma".
-let rec C_rect (P: (C \to Type[0])) (f: (\forall (n: nat).(P (CSort n))))
-(f0: (\forall (c: C).((P c) \to (\forall (k: K).(\forall (t: T).(P (CHead c k
-t))))))) (c: C) on c: P c \def match c with [(CSort n) \Rightarrow (f n) |
-(CHead c0 k t) \Rightarrow (f0 c0 ((C_rect P f f0) c0) k t)].
+implied rec lemma C_rect (P: (C \to Type[0])) (f: (\forall (n: nat).(P (CSort
+n)))) (f0: (\forall (c: C).((P c) \to (\forall (k: K).(\forall (t: T).(P
+(CHead c k t))))))) (c: C) on c: P c \def match c with [(CSort n) \Rightarrow
+(f n) | (CHead c0 k t) \Rightarrow (f0 c0 ((C_rect P f f0) c0) k t)].
-theorem C_ind:
+implied lemma C_ind:
\forall (P: ((C \to Prop))).(((\forall (n: nat).(P (CSort n)))) \to
(((\forall (c: C).((P c) \to (\forall (k: K).(\forall (t: T).(P (CHead c k
t))))))) \to (\forall (c: C).(P c))))
\def
\lambda (P: ((C \to Prop))).(C_rect P).
-theorem clt_wf__q_ind:
+fact clt_wf__q_ind:
\forall (P: ((C \to Prop))).(((\forall (n: nat).((\lambda (P0: ((C \to
Prop))).(\lambda (n0: nat).(\forall (c: C).((eq nat (cweight c) n0) \to (P0
c))))) P n))) \to (\forall (c: C).(P c)))
n) \to (P c)))))).(\lambda (c: C).(H (cweight c) c (refl_equal nat (cweight
c)))))).
-theorem clt_wf_ind:
+lemma clt_wf_ind:
\forall (P: ((C \to Prop))).(((\forall (c: C).(((\forall (d: C).((clt d c)
\to (P d)))) \to (P c)))) \to (\forall (c: C).(P c)))
\def