-(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: