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
\lambda (g: G).(\lambda (c1: C).(\lambda (t: T).(\lambda (a: A).(\lambda (H:
-(arity g c1 t a)).(let TMP_1 \def (\lambda (c: C).(\lambda (t0: T).(\lambda
-(a0: A).(\forall (c2: C).((cimp c c2) \to (arity g c2 t0 a0)))))) in (let
-TMP_2 \def (\lambda (c: C).(\lambda (n: nat).(\lambda (c2: C).(\lambda (_:
-(cimp c c2)).(arity_sort g c2 n))))) in (let TMP_41 \def (\lambda (c:
-C).(\lambda (d: C).(\lambda (u: T).(\lambda (i: nat).(\lambda (H0: (getl i c
-(CHead d (Bind Abbr) u))).(\lambda (a0: A).(\lambda (_: (arity g d u
-a0)).(\lambda (H2: ((\forall (c2: C).((cimp d c2) \to (arity g c2 u
-a0))))).(\lambda (c2: C).(\lambda (H3: (cimp c c2)).(let H_x \def (H3 Abbr d
-u i H0) in (let H4 \def H_x in (let TMP_5 \def (\lambda (d2: C).(let TMP_3
-\def (Bind Abbr) in (let TMP_4 \def (CHead d2 TMP_3 u) in (getl i c2
-TMP_4)))) in (let TMP_6 \def (TLRef i) in (let TMP_7 \def (arity g c2 TMP_6
-a0) in (let TMP_40 \def (\lambda (x: C).(\lambda (H5: (getl i c2 (CHead x
-(Bind Abbr) u))).(let H_x0 \def (cimp_getl_conf c c2 H3 Abbr d u i H0) in
-(let H6 \def H_x0 in (let TMP_8 \def (\lambda (d2: C).(cimp d d2)) in (let
-TMP_11 \def (\lambda (d2: C).(let TMP_9 \def (Bind Abbr) in (let TMP_10 \def
-(CHead d2 TMP_9 u) in (getl i c2 TMP_10)))) in (let TMP_12 \def (TLRef i) in
-(let TMP_13 \def (arity g c2 TMP_12 a0) in (let TMP_39 \def (\lambda (x0:
-C).(\lambda (H7: (cimp d x0)).(\lambda (H8: (getl i c2 (CHead x0 (Bind Abbr)
-u))).(let TMP_14 \def (Bind Abbr) in (let TMP_15 \def (CHead x TMP_14 u) in
-(let TMP_16 \def (\lambda (c0: C).(getl i c2 c0)) in (let TMP_17 \def (Bind
-Abbr) in (let TMP_18 \def (CHead x0 TMP_17 u) in (let TMP_19 \def (Bind Abbr)
-in (let TMP_20 \def (CHead x TMP_19 u) in (let TMP_21 \def (Bind Abbr) in
-(let TMP_22 \def (CHead x0 TMP_21 u) in (let TMP_23 \def (getl_mono c2 TMP_20
-i H5 TMP_22 H8) in (let H9 \def (eq_ind C TMP_15 TMP_16 H5 TMP_18 TMP_23) in
-(let TMP_24 \def (\lambda (e: C).(match e with [(CSort _) \Rightarrow x |
-(CHead c0 _ _) \Rightarrow c0])) in (let TMP_25 \def (Bind Abbr) in (let
-TMP_26 \def (CHead x TMP_25 u) in (let TMP_27 \def (Bind Abbr) in (let TMP_28
-\def (CHead x0 TMP_27 u) in (let TMP_29 \def (Bind Abbr) in (let TMP_30 \def
-(CHead x TMP_29 u) in (let TMP_31 \def (Bind Abbr) in (let TMP_32 \def (CHead
-x0 TMP_31 u) in (let TMP_33 \def (getl_mono c2 TMP_30 i H5 TMP_32 H8) in (let
-H10 \def (f_equal C C TMP_24 TMP_26 TMP_28 TMP_33) in (let TMP_36 \def
-(\lambda (c0: C).(let TMP_34 \def (Bind Abbr) in (let TMP_35 \def (CHead c0
-TMP_34 u) in (getl i c2 TMP_35)))) in (let H11 \def (eq_ind_r C x0 TMP_36 H9
-x H10) in (let TMP_37 \def (\lambda (c0: C).(cimp d c0)) in (let H12 \def
-(eq_ind_r C x0 TMP_37 H7 x H10) in (let TMP_38 \def (H2 x H12) in (arity_abbr
-g c2 x u i H11 a0 TMP_38))))))))))))))))))))))))))))))) in (ex2_ind C TMP_8
-TMP_11 TMP_13 TMP_39 H6)))))))))) in (ex_ind C TMP_5 TMP_7 TMP_40
-H4))))))))))))))))) in (let TMP_80 \def (\lambda (c: C).(\lambda (d:
+(arity g c1 t a)).(arity_ind g (\lambda (c: C).(\lambda (t0: T).(\lambda (a0:
+A).(\forall (c2: C).((cimp c c2) \to (arity g c2 t0 a0)))))) (\lambda (c:
+C).(\lambda (n: nat).(\lambda (c2: C).(\lambda (_: (cimp c c2)).(arity_sort g
+c2 n))))) (\lambda (c: C).(\lambda (d: C).(\lambda (u: T).(\lambda (i:
+nat).(\lambda (H0: (getl i c (CHead d (Bind Abbr) u))).(\lambda (a0:
+A).(\lambda (_: (arity g d u a0)).(\lambda (H2: ((\forall (c2: C).((cimp d
+c2) \to (arity g c2 u a0))))).(\lambda (c2: C).(\lambda (H3: (cimp c
+c2)).(let H_x \def (H3 Abbr d u i H0) in (let H4 \def H_x in (ex_ind C
+(\lambda (d2: C).(getl i c2 (CHead d2 (Bind Abbr) u))) (arity g c2 (TLRef i)
+a0) (\lambda (x: C).(\lambda (H5: (getl i c2 (CHead x (Bind Abbr) u))).(let
+H_x0 \def (cimp_getl_conf c c2 H3 Abbr 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 Abbr) u))) (arity g c2 (TLRef i) a0) (\lambda (x0: C).(\lambda (H7:
+(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 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 (let TMP_44 \def (\lambda (d2: C).(let TMP_42
-\def (Bind Abst) in (let TMP_43 \def (CHead d2 TMP_42 u) in (getl i c2
-TMP_43)))) in (let TMP_45 \def (TLRef i) in (let TMP_46 \def (arity g c2
-TMP_45 a0) in (let TMP_79 \def (\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 (let TMP_47 \def (\lambda (d2: C).(cimp d d2)) in
-(let TMP_50 \def (\lambda (d2: C).(let TMP_48 \def (Bind Abst) in (let TMP_49
-\def (CHead d2 TMP_48 u) in (getl i c2 TMP_49)))) in (let TMP_51 \def (TLRef
-i) in (let TMP_52 \def (arity g c2 TMP_51 a0) in (let TMP_78 \def (\lambda
-(x0: C).(\lambda (H7: (cimp d x0)).(\lambda (H8: (getl i c2 (CHead x0 (Bind
-Abst) u))).(let TMP_53 \def (Bind Abst) in (let TMP_54 \def (CHead x TMP_53
-u) in (let TMP_55 \def (\lambda (c0: C).(getl i c2 c0)) in (let TMP_56 \def
-(Bind Abst) in (let TMP_57 \def (CHead x0 TMP_56 u) in (let TMP_58 \def (Bind
-Abst) in (let TMP_59 \def (CHead x TMP_58 u) in (let TMP_60 \def (Bind Abst)
-in (let TMP_61 \def (CHead x0 TMP_60 u) in (let TMP_62 \def (getl_mono c2
-TMP_59 i H5 TMP_61 H8) in (let H9 \def (eq_ind C TMP_54 TMP_55 H5 TMP_57
-TMP_62) in (let TMP_63 \def (\lambda (e: C).(match e with [(CSort _)
-\Rightarrow x | (CHead c0 _ _) \Rightarrow c0])) in (let TMP_64 \def (Bind
-Abst) in (let TMP_65 \def (CHead x TMP_64 u) in (let TMP_66 \def (Bind Abst)
-in (let TMP_67 \def (CHead x0 TMP_66 u) in (let TMP_68 \def (Bind Abst) in
-(let TMP_69 \def (CHead x TMP_68 u) in (let TMP_70 \def (Bind Abst) in (let
-TMP_71 \def (CHead x0 TMP_70 u) in (let TMP_72 \def (getl_mono c2 TMP_69 i H5
-TMP_71 H8) in (let H10 \def (f_equal C C TMP_63 TMP_65 TMP_67 TMP_72) in (let
-TMP_75 \def (\lambda (c0: C).(let TMP_73 \def (Bind Abst) in (let TMP_74 \def
-(CHead c0 TMP_73 u) in (getl i c2 TMP_74)))) in (let H11 \def (eq_ind_r C x0
-TMP_75 H9 x H10) in (let TMP_76 \def (\lambda (c0: C).(cimp d c0)) in (let
-H12 \def (eq_ind_r C x0 TMP_76 H7 x H10) in (let TMP_77 \def (H2 x H12) in
-(arity_abst g c2 x u i H11 a0 TMP_77))))))))))))))))))))))))))))))) in
-(ex2_ind C TMP_47 TMP_50 TMP_52 TMP_78 H6)))))))))) in (ex_ind C TMP_44
-TMP_46 TMP_79 H4))))))))))))))))) in (let TMP_86 \def (\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
+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
+c2)).(arity_bind g b H0 c2 u a1 (H2 c2 H5) t0 a2 (H4 (CHead c2 (Bind b) u)
+(cimp_bind c c2 H5 b u)))))))))))))))) (\lambda (c: C).(\lambda (u:
+T).(\lambda (a1: A).(\lambda (_: (arity g c u (asucc g a1))).(\lambda (H1:
+((\forall (c2: C).((cimp c c2) \to (arity g c2 u (asucc g a1)))))).(\lambda
+(t0: T).(\lambda (a2: A).(\lambda (_: (arity g (CHead c (Bind Abst) u) t0
+a2)).(\lambda (H3: ((\forall (c2: C).((cimp (CHead c (Bind Abst) u) c2) \to
+(arity g c2 t0 a2))))).(\lambda (c2: C).(\lambda (H4: (cimp c
+c2)).(arity_head g c2 u a1 (H1 c2 H4) t0 a2 (H3 (CHead c2 (Bind Abst) u)
+(cimp_bind c c2 H4 Abst u)))))))))))))) (\lambda (c: C).(\lambda (u:
+T).(\lambda (a1: A).(\lambda (_: (arity g c u a1)).(\lambda (H1: ((\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 c2)).(let TMP_81 \def (H2 c2 H5) in (let TMP_82
-\def (Bind b) in (let TMP_83 \def (CHead c2 TMP_82 u) in (let TMP_84 \def
-(cimp_bind c c2 H5 b u) in (let TMP_85 \def (H4 TMP_83 TMP_84) in (arity_bind
-g b H0 c2 u a1 TMP_81 t0 a2 TMP_85))))))))))))))))))) in (let TMP_92 \def
-(\lambda (c: C).(\lambda (u: T).(\lambda (a1: A).(\lambda (_: (arity g c u
-(asucc g a1))).(\lambda (H1: ((\forall (c2: C).((cimp c c2) \to (arity g c2 u
-(asucc g a1)))))).(\lambda (t0: T).(\lambda (a2: A).(\lambda (_: (arity g
-(CHead c (Bind Abst) u) t0 a2)).(\lambda (H3: ((\forall (c2: C).((cimp (CHead
-c (Bind Abst) u) c2) \to (arity g c2 t0 a2))))).(\lambda (c2: C).(\lambda
-(H4: (cimp c c2)).(let TMP_87 \def (H1 c2 H4) in (let TMP_88 \def (Bind Abst)
-in (let TMP_89 \def (CHead c2 TMP_88 u) in (let TMP_90 \def (cimp_bind c c2
-H4 Abst u) in (let TMP_91 \def (H3 TMP_89 TMP_90) in (arity_head g c2 u a1
-TMP_87 t0 a2 TMP_91))))))))))))))))) in (let TMP_95 \def (\lambda (c:
-C).(\lambda (u: T).(\lambda (a1: A).(\lambda (_: (arity g c u a1)).(\lambda
-(H1: ((\forall (c2: C).((cimp c c2) \to (arity g c2 u a1))))).(\lambda (t0:
-T).(\lambda (a2: A).(\lambda (_: (arity g c t0 (AHead a1 a2))).(\lambda (H3:
-((\forall (c2: C).((cimp c c2) \to (arity g c2 t0 (AHead a1 a2)))))).(\lambda
-(c2: C).(\lambda (H4: (cimp c c2)).(let TMP_93 \def (H1 c2 H4) in (let TMP_94
-\def (H3 c2 H4) in (arity_appl g c2 u a1 TMP_93 t0 a2 TMP_94)))))))))))))) in
-(let TMP_98 \def (\lambda (c: C).(\lambda (u: T).(\lambda (a0: A).(\lambda
-(_: (arity g c u (asucc g a0))).(\lambda (H1: ((\forall (c2: C).((cimp c c2)
-\to (arity g c2 u (asucc g a0)))))).(\lambda (t0: T).(\lambda (_: (arity g c
-t0 a0)).(\lambda (H3: ((\forall (c2: C).((cimp c c2) \to (arity g c2 t0
-a0))))).(\lambda (c2: C).(\lambda (H4: (cimp c c2)).(let TMP_96 \def (H1 c2
-H4) in (let TMP_97 \def (H3 c2 H4) in (arity_cast g c2 u a0 TMP_96 t0
-TMP_97))))))))))))) in (let TMP_100 \def (\lambda (c: C).(\lambda (t0:
-T).(\lambda (a1: A).(\lambda (_: (arity g c t0 a1)).(\lambda (H1: ((\forall
-(c2: 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)).(let TMP_99
-\def (H1 c2 H3) in (arity_repl g c2 t0 a1 TMP_99 a2 H2))))))))))) in
-(arity_ind g TMP_1 TMP_2 TMP_41 TMP_80 TMP_86 TMP_92 TMP_95 TMP_98 TMP_100 c1
-t a H)))))))))))))).
+A).(\lambda (_: (arity g c t0 (AHead a1 a2))).(\lambda (H3: ((\forall (c2:
+C).((cimp c c2) \to (arity g c2 t0 (AHead a1 a2)))))).(\lambda (c2:
+C).(\lambda (H4: (cimp c c2)).(arity_appl g c2 u a1 (H1 c2 H4) t0 a2 (H3 c2
+H4))))))))))))) (\lambda (c: C).(\lambda (u: T).(\lambda (a0: A).(\lambda (_:
+(arity g c u (asucc g a0))).(\lambda (H1: ((\forall (c2: C).((cimp c c2) \to
+(arity g c2 u (asucc g a0)))))).(\lambda (t0: T).(\lambda (_: (arity g c t0
+a0)).(\lambda (H3: ((\forall (c2: C).((cimp c c2) \to (arity g c2 t0
+a0))))).(\lambda (c2: C).(\lambda (H4: (cimp c c2)).(arity_cast g c2 u a0 (H1
+c2 H4) t0 (H3 c2 H4)))))))))))) (\lambda (c: C).(\lambda (t0: T).(\lambda
+(a1: A).(\lambda (_: (arity g c t0 a1)).(\lambda (H1: ((\forall (c2:
+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))))).
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