(* This file was automatically generated: do not edit *********************)
-include "Basic-1/arity/defs.ma".
+include "basic_1/arity/fwd.ma".
-include "Basic-1/cimp/props.ma".
+include "basic_1/cimp/props.ma".
-theorem arity_cimp_conf:
+lemma arity_cimp_conf:
\forall (g: G).(\forall (c1: C).(\forall (t: T).(\forall (a: A).((arity g c1
t a) \to (\forall (c2: C).((cimp c1 c2) \to (arity g c2 t a)))))))
\def
(cimp d x0)).(\lambda (H8: (getl i c2 (CHead x0 (Bind Abbr) u))).(let H9 \def
(eq_ind C (CHead x (Bind Abbr) u) (\lambda (c0: C).(getl i c2 c0)) H5 (CHead
x0 (Bind Abbr) u) (getl_mono c2 (CHead x (Bind Abbr) u) i H5 (CHead x0 (Bind
-Abbr) u) H8)) in (let H10 \def (f_equal C C (\lambda (e: C).(match e in C
-return (\lambda (_: C).C) with [(CSort _) \Rightarrow x | (CHead c0 _ _)
-\Rightarrow c0])) (CHead x (Bind Abbr) u) (CHead x0 (Bind Abbr) u) (getl_mono
-c2 (CHead x (Bind Abbr) u) i H5 (CHead x0 (Bind Abbr) u) H8)) in (let H11
-\def (eq_ind_r C x0 (\lambda (c0: C).(getl i c2 (CHead c0 (Bind Abbr) u))) H9
-x H10) in (let H12 \def (eq_ind_r C x0 (\lambda (c0: C).(cimp d c0)) H7 x
-H10) in (arity_abbr g c2 x u i H11 a0 (H2 x H12))))))))) H6)))))
-H4))))))))))))) (\lambda (c: C).(\lambda (d: C).(\lambda (u: T).(\lambda (i:
-nat).(\lambda (H0: (getl i c (CHead d (Bind Abst) u))).(\lambda (a0:
-A).(\lambda (_: (arity g d u (asucc g a0))).(\lambda (H2: ((\forall (c2:
-C).((cimp d c2) \to (arity g c2 u (asucc g a0)))))).(\lambda (c2: C).(\lambda
-(H3: (cimp c c2)).(let H_x \def (H3 Abst d u i H0) in (let H4 \def H_x in
-(ex_ind C (\lambda (d2: C).(getl i c2 (CHead d2 (Bind Abst) u))) (arity g c2
-(TLRef i) a0) (\lambda (x: C).(\lambda (H5: (getl i c2 (CHead x (Bind Abst)
-u))).(let H_x0 \def (cimp_getl_conf c c2 H3 Abst d u i H0) in (let H6 \def
-H_x0 in (ex2_ind C (\lambda (d2: C).(cimp d d2)) (\lambda (d2: C).(getl i c2
-(CHead d2 (Bind Abst) u))) (arity g c2 (TLRef i) a0) (\lambda (x0:
-C).(\lambda (H7: (cimp d x0)).(\lambda (H8: (getl i c2 (CHead x0 (Bind Abst)
-u))).(let H9 \def (eq_ind C (CHead x (Bind Abst) u) (\lambda (c0: C).(getl i
-c2 c0)) H5 (CHead x0 (Bind Abst) u) (getl_mono c2 (CHead x (Bind Abst) u) i
-H5 (CHead x0 (Bind Abst) u) H8)) in (let H10 \def (f_equal C C (\lambda (e:
-C).(match e in C return (\lambda (_: C).C) with [(CSort _) \Rightarrow x |
-(CHead c0 _ _) \Rightarrow c0])) (CHead x (Bind Abst) u) (CHead x0 (Bind
-Abst) u) (getl_mono c2 (CHead x (Bind Abst) u) i H5 (CHead x0 (Bind Abst) u)
-H8)) in (let H11 \def (eq_ind_r C x0 (\lambda (c0: C).(getl i c2 (CHead c0
-(Bind Abst) u))) H9 x H10) in (let H12 \def (eq_ind_r C x0 (\lambda (c0:
-C).(cimp d c0)) H7 x H10) in (arity_abst g c2 x u i H11 a0 (H2 x H12)))))))))
-H6))))) H4))))))))))))) (\lambda (b: B).(\lambda (H0: (not (eq B b
-Abst))).(\lambda (c: C).(\lambda (u: T).(\lambda (a1: A).(\lambda (_: (arity
-g c u a1)).(\lambda (H2: ((\forall (c2: C).((cimp c c2) \to (arity g c2 u
+Abbr) u) H8)) in (let H10 \def (f_equal C C (\lambda (e: C).(match e with
+[(CSort _) \Rightarrow x | (CHead c0 _ _) \Rightarrow c0])) (CHead x (Bind
+Abbr) u) (CHead x0 (Bind Abbr) u) (getl_mono c2 (CHead x (Bind Abbr) u) i H5
+(CHead x0 (Bind Abbr) u) H8)) in (let H11 \def (eq_ind_r C x0 (\lambda (c0:
+C).(getl i c2 (CHead c0 (Bind Abbr) u))) H9 x H10) in (let H12 \def (eq_ind_r
+C x0 (\lambda (c0: C).(cimp d c0)) H7 x H10) in (arity_abbr g c2 x u i H11 a0
+(H2 x H12))))))))) H6))))) H4))))))))))))) (\lambda (c: C).(\lambda (d:
+C).(\lambda (u: T).(\lambda (i: nat).(\lambda (H0: (getl i c (CHead d (Bind
+Abst) u))).(\lambda (a0: A).(\lambda (_: (arity g d u (asucc g a0))).(\lambda
+(H2: ((\forall (c2: C).((cimp d c2) \to (arity g c2 u (asucc g
+a0)))))).(\lambda (c2: C).(\lambda (H3: (cimp c c2)).(let H_x \def (H3 Abst d
+u i H0) in (let H4 \def H_x in (ex_ind C (\lambda (d2: C).(getl i c2 (CHead
+d2 (Bind Abst) u))) (arity g c2 (TLRef i) a0) (\lambda (x: C).(\lambda (H5:
+(getl i c2 (CHead x (Bind Abst) u))).(let H_x0 \def (cimp_getl_conf c c2 H3
+Abst d u i H0) in (let H6 \def H_x0 in (ex2_ind C (\lambda (d2: C).(cimp d
+d2)) (\lambda (d2: C).(getl i c2 (CHead d2 (Bind Abst) u))) (arity g c2
+(TLRef i) a0) (\lambda (x0: C).(\lambda (H7: (cimp d x0)).(\lambda (H8: (getl
+i c2 (CHead x0 (Bind Abst) u))).(let H9 \def (eq_ind C (CHead x (Bind Abst)
+u) (\lambda (c0: C).(getl i c2 c0)) H5 (CHead x0 (Bind Abst) u) (getl_mono c2
+(CHead x (Bind Abst) u) i H5 (CHead x0 (Bind Abst) u) H8)) in (let H10 \def
+(f_equal C C (\lambda (e: C).(match e with [(CSort _) \Rightarrow x | (CHead
+c0 _ _) \Rightarrow c0])) (CHead x (Bind Abst) u) (CHead x0 (Bind Abst) u)
+(getl_mono c2 (CHead x (Bind Abst) u) i H5 (CHead x0 (Bind Abst) u) H8)) in
+(let H11 \def (eq_ind_r C x0 (\lambda (c0: C).(getl i c2 (CHead c0 (Bind
+Abst) u))) H9 x H10) in (let H12 \def (eq_ind_r C x0 (\lambda (c0: C).(cimp d
+c0)) H7 x H10) in (arity_abst g c2 x u i H11 a0 (H2 x H12))))))))) H6)))))
+H4))))))))))))) (\lambda (b: B).(\lambda (H0: (not (eq B b Abst))).(\lambda
+(c: C).(\lambda (u: T).(\lambda (a1: A).(\lambda (_: (arity g c u
+a1)).(\lambda (H2: ((\forall (c2: C).((cimp c c2) \to (arity g c2 u
a1))))).(\lambda (t0: T).(\lambda (a2: A).(\lambda (_: (arity g (CHead c
(Bind b) u) t0 a2)).(\lambda (H4: ((\forall (c2: C).((cimp (CHead c (Bind b)
u) c2) \to (arity g c2 t0 a2))))).(\lambda (c2: C).(\lambda (H5: (cimp c
C).((cimp c c2) \to (arity g c2 t0 a1))))).(\lambda (a2: A).(\lambda (H2:
(leq g a1 a2)).(\lambda (c2: C).(\lambda (H3: (cimp c c2)).(arity_repl g c2
t0 a1 (H1 c2 H3) a2 H2)))))))))) c1 t a H))))).
-(* COMMENTS
-Initial nodes: 1505
-END *)