X-Git-Url: http://matita.cs.unibo.it/gitweb/?a=blobdiff_plain;ds=sidebyside;f=matita%2Fmatita%2Fcontribs%2Flambdadelta%2Fbasic_1%2Fcsuba%2Farity.ma;h=7b35a4381bb36b2440172e20b3e2a68ca3c96b78;hb=1aca50505c3ce6c76dd7d20d00e358707caffd4a;hp=fe021cd0f3d05df8f88e29a6a0056ce28164e531;hpb=88a68a9c334646bc17314d5327cd3b790202acd6;p=helm.git

diff --git a/matita/matita/contribs/lambdadelta/basic_1/csuba/arity.ma b/matita/matita/contribs/lambdadelta/basic_1/csuba/arity.ma
index fe021cd0f..7b35a4381 100644
--- a/matita/matita/contribs/lambdadelta/basic_1/csuba/arity.ma
+++ b/matita/matita/contribs/lambdadelta/basic_1/csuba/arity.ma
@@ -14,15 +14,15 @@
 
 (* This file was automatically generated: do not edit *********************)
 
-include "Basic-1/csuba/getl.ma".
+include "basic_1/csuba/getl.ma".
 
-include "Basic-1/csuba/props.ma".
+include "basic_1/csuba/props.ma".
 
-include "Basic-1/arity/props.ma".
+include "basic_1/arity/fwd.ma".
 
-include "Basic-1/csubv/getl.ma".
+include "basic_1/csubv/getl.ma".
 
-theorem csuba_arity:
+lemma csuba_arity:
  \forall (g: G).(\forall (c1: C).(\forall (t: T).(\forall (a: A).((arity g c1 
 t a) \to (\forall (c2: C).((csuba g c1 c2) \to (arity g c2 t a)))))))
 \def
@@ -100,11 +100,8 @@ H4)))))))))))) (\lambda (c: C).(\lambda (t0: T).(\lambda (a1: A).(\lambda (_:
 g c2 t0 a1))))).(\lambda (a2: A).(\lambda (H2: (leq g a1 a2)).(\lambda (c2: 
 C).(\lambda (H3: (csuba g c c2)).(arity_repl g c2 t0 a1 (H1 c2 H3) a2 
 H2)))))))))) c1 t a H))))).
-(* COMMENTS
-Initial nodes: 1505
-END *)
 
-theorem csuba_arity_rev:
+lemma csuba_arity_rev:
  \forall (g: G).(\forall (c1: C).(\forall (t: T).(\forall (a: A).((arity g c1 
 t a) \to (\forall (c2: C).((csuba g c2 c1) \to ((csubv c2 c1) \to (arity g c2 
 t a))))))))
@@ -139,94 +136,89 @@ B).(\lambda (d2: C).(\lambda (_: T).(csubv x d2)))) (\lambda (b2: B).(\lambda
 (H10: (csubv x x1)).(\lambda (H11: (getl i c (CHead x1 (Bind x0) x2))).(let 
 H12 \def (eq_ind C (CHead d (Bind Abbr) u) (\lambda (c0: C).(getl i c c0)) H0 
 (CHead x1 (Bind x0) x2) (getl_mono c (CHead d (Bind Abbr) u) i H0 (CHead x1 
-(Bind x0) x2) H11)) in (let H13 \def (f_equal C C (\lambda (e: C).(match e in 
-C return (\lambda (_: C).C) with [(CSort _) \Rightarrow d | (CHead c0 _ _) 
-\Rightarrow c0])) (CHead d (Bind Abbr) u) (CHead x1 (Bind x0) x2) (getl_mono 
-c (CHead d (Bind Abbr) u) i H0 (CHead x1 (Bind x0) x2) H11)) in ((let H14 
-\def (f_equal C B (\lambda (e: C).(match e in C return (\lambda (_: C).B) 
-with [(CSort _) \Rightarrow Abbr | (CHead _ k _) \Rightarrow (match k in K 
-return (\lambda (_: K).B) with [(Bind b) \Rightarrow b | (Flat _) \Rightarrow 
-Abbr])])) (CHead d (Bind Abbr) u) (CHead x1 (Bind x0) x2) (getl_mono c (CHead 
-d (Bind Abbr) u) i H0 (CHead x1 (Bind x0) x2) H11)) in ((let H15 \def 
-(f_equal C T (\lambda (e: C).(match e in C return (\lambda (_: C).T) with 
-[(CSort _) \Rightarrow u | (CHead _ _ t0) \Rightarrow t0])) (CHead d (Bind 
-Abbr) u) (CHead x1 (Bind x0) x2) (getl_mono c (CHead d (Bind Abbr) u) i H0 
-(CHead x1 (Bind x0) x2) H11)) in (\lambda (H16: (eq B Abbr x0)).(\lambda 
-(H17: (eq C d x1)).(let H18 \def (eq_ind_r T x2 (\lambda (t0: T).(getl i c 
-(CHead x1 (Bind x0) t0))) H12 u H15) in (let H19 \def (eq_ind_r C x1 (\lambda 
-(c0: C).(getl i c (CHead c0 (Bind x0) u))) H18 d H17) in (let H20 \def 
-(eq_ind_r C x1 (\lambda (c0: C).(csubv x c0)) H10 d H17) in (let H21 \def 
-(eq_ind_r B x0 (\lambda (b: B).(getl i c (CHead d (Bind b) u))) H19 Abbr H16) 
-in (arity_abbr g c2 x u i H7 a0 (H2 x H8 H20))))))))) H14)) H13)))))))) 
-H9)))))) H6)) (\lambda (H6: (ex4_3 C T A (\lambda (d2: C).(\lambda (u2: 
-T).(\lambda (_: A).(getl i c2 (CHead d2 (Bind Abst) u2))))) (\lambda (d2: 
-C).(\lambda (_: T).(\lambda (_: A).(csuba g d2 d)))) (\lambda (d2: 
-C).(\lambda (u2: T).(\lambda (a1: A).(arity g d2 u2 (asucc g a1))))) (\lambda 
-(_: C).(\lambda (_: T).(\lambda (a1: A).(arity g d u a1)))))).(ex4_3_ind C T 
-A (\lambda (d2: C).(\lambda (u2: T).(\lambda (_: A).(getl i c2 (CHead d2 
-(Bind Abst) u2))))) (\lambda (d2: C).(\lambda (_: T).(\lambda (_: A).(csuba g 
-d2 d)))) (\lambda (d2: C).(\lambda (u2: T).(\lambda (a1: A).(arity g d2 u2 
-(asucc g a1))))) (\lambda (_: C).(\lambda (_: T).(\lambda (a1: A).(arity g d 
-u a1)))) (arity g c2 (TLRef i) a0) (\lambda (x0: C).(\lambda (x1: T).(\lambda 
-(x2: A).(\lambda (H7: (getl i c2 (CHead x0 (Bind Abst) x1))).(\lambda (_: 
-(csuba g x0 d)).(\lambda (H9: (arity g x0 x1 (asucc g x2))).(\lambda (H10: 
-(arity g d u x2)).(arity_repl g c2 (TLRef i) x2 (arity_abst g c2 x0 x1 i H7 
-x2 H9) a0 (arity_mono g d u x2 H10 a0 H1))))))))) H6)) (\lambda (H6: (ex2_2 C 
-T (\lambda (d2: C).(\lambda (u2: T).(getl i c2 (CHead d2 (Bind Void) u2)))) 
-(\lambda (d2: C).(\lambda (_: T).(csuba g d2 d))))).(ex2_2_ind C T (\lambda 
-(d2: C).(\lambda (u2: T).(getl i c2 (CHead d2 (Bind Void) u2)))) (\lambda 
-(d2: C).(\lambda (_: T).(csuba g d2 d))) (arity g c2 (TLRef i) a0) (\lambda 
-(x0: C).(\lambda (x1: T).(\lambda (H7: (getl i c2 (CHead x0 (Bind Void) 
-x1))).(\lambda (_: (csuba g x0 d)).(let H_x0 \def (csubv_getl_conf_void c2 c 
-H4 x0 x1 i H7) in (let H9 \def H_x0 in (ex2_2_ind C T (\lambda (d2: 
-C).(\lambda (_: T).(csubv x0 d2))) (\lambda (d2: C).(\lambda (v2: T).(getl i 
-c (CHead d2 (Bind Void) v2)))) (arity g c2 (TLRef i) a0) (\lambda (x2: 
-C).(\lambda (x3: T).(\lambda (_: (csubv x0 x2)).(\lambda (H11: (getl i c 
-(CHead x2 (Bind Void) x3))).(let H12 \def (eq_ind C (CHead d (Bind Abbr) u) 
-(\lambda (c0: C).(getl i c c0)) H0 (CHead x2 (Bind Void) x3) (getl_mono c 
-(CHead d (Bind Abbr) u) i H0 (CHead x2 (Bind Void) x3) H11)) in (let H13 \def 
-(eq_ind C (CHead d (Bind Abbr) u) (\lambda (ee: C).(match ee in C return 
-(\lambda (_: C).Prop) with [(CSort _) \Rightarrow False | (CHead _ k _) 
-\Rightarrow (match k in K return (\lambda (_: K).Prop) with [(Bind b) 
-\Rightarrow (match b in B return (\lambda (_: B).Prop) with [Abbr \Rightarrow 
-True | Abst \Rightarrow False | Void \Rightarrow False]) | (Flat _) 
-\Rightarrow False])])) I (CHead x2 (Bind Void) x3) (getl_mono c (CHead d 
-(Bind Abbr) u) i H0 (CHead x2 (Bind Void) x3) H11)) in (False_ind (arity g c2 
-(TLRef i) a0) H13))))))) H9))))))) H6)) H5)))))))))))))) (\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).((csuba g c2 d) \to ((csubv c2 d) \to 
-(arity g c2 u (asucc g a0))))))).(\lambda (c2: C).(\lambda (H3: (csuba g c2 
-c)).(\lambda (H4: (csubv c2 c)).(let H_x \def (csuba_getl_abst_rev g c d u i 
-H0 c2 H3) in (let H5 \def H_x in (or_ind (ex2 C (\lambda (d2: C).(getl i c2 
-(CHead d2 (Bind Abst) u))) (\lambda (d2: C).(csuba g d2 d))) (ex2_2 C T 
-(\lambda (d2: C).(\lambda (u2: T).(getl i c2 (CHead d2 (Bind Void) u2)))) 
-(\lambda (d2: C).(\lambda (_: T).(csuba g d2 d)))) (arity g c2 (TLRef i) a0) 
-(\lambda (H6: (ex2 C (\lambda (d2: C).(getl i c2 (CHead d2 (Bind Abst) u))) 
-(\lambda (d2: C).(csuba g d2 d)))).(ex2_ind C (\lambda (d2: C).(getl i c2 
-(CHead d2 (Bind Abst) u))) (\lambda (d2: C).(csuba g d2 d)) (arity g c2 
-(TLRef i) a0) (\lambda (x: C).(\lambda (H7: (getl i c2 (CHead x (Bind Abst) 
-u))).(\lambda (H8: (csuba g x d)).(let H_x0 \def (csubv_getl_conf c2 c H4 
-Abst x u i H7) in (let H9 \def H_x0 in (ex2_3_ind B C T (\lambda (_: 
-B).(\lambda (d2: C).(\lambda (_: T).(csubv x d2)))) (\lambda (b2: B).(\lambda 
-(d2: C).(\lambda (v2: T).(getl i c (CHead d2 (Bind b2) v2))))) (arity g c2 
-(TLRef i) a0) (\lambda (x0: B).(\lambda (x1: C).(\lambda (x2: T).(\lambda 
-(H10: (csubv x x1)).(\lambda (H11: (getl i c (CHead x1 (Bind x0) x2))).(let 
-H12 \def (eq_ind C (CHead d (Bind Abst) u) (\lambda (c0: C).(getl i c c0)) H0 
+(Bind x0) x2) H11)) in (let H13 \def (f_equal C C (\lambda (e: C).(match e 
+with [(CSort _) \Rightarrow d | (CHead c0 _ _) \Rightarrow c0])) (CHead d 
+(Bind Abbr) u) (CHead x1 (Bind x0) x2) (getl_mono c (CHead d (Bind Abbr) u) i 
+H0 (CHead x1 (Bind x0) x2) H11)) in ((let H14 \def (f_equal C B (\lambda (e: 
+C).(match e with [(CSort _) \Rightarrow Abbr | (CHead _ k _) \Rightarrow 
+(match k with [(Bind b) \Rightarrow b | (Flat _) \Rightarrow Abbr])])) (CHead 
+d (Bind Abbr) u) (CHead x1 (Bind x0) x2) (getl_mono c (CHead d (Bind Abbr) u) 
+i H0 (CHead x1 (Bind x0) x2) H11)) in ((let H15 \def (f_equal C T (\lambda 
+(e: C).(match e with [(CSort _) \Rightarrow u | (CHead _ _ t0) \Rightarrow 
+t0])) (CHead d (Bind Abbr) u) (CHead x1 (Bind x0) x2) (getl_mono c (CHead d 
+(Bind Abbr) u) i H0 (CHead x1 (Bind x0) x2) H11)) in (\lambda (H16: (eq B 
+Abbr x0)).(\lambda (H17: (eq C d x1)).(let H18 \def (eq_ind_r T x2 (\lambda 
+(t0: T).(getl i c (CHead x1 (Bind x0) t0))) H12 u H15) in (let H19 \def 
+(eq_ind_r C x1 (\lambda (c0: C).(getl i c (CHead c0 (Bind x0) u))) H18 d H17) 
+in (let H20 \def (eq_ind_r C x1 (\lambda (c0: C).(csubv x c0)) H10 d H17) in 
+(let H21 \def (eq_ind_r B x0 (\lambda (b: B).(getl i c (CHead d (Bind b) u))) 
+H19 Abbr H16) in (arity_abbr g c2 x u i H7 a0 (H2 x H8 H20))))))))) H14)) 
+H13)))))))) H9)))))) H6)) (\lambda (H6: (ex4_3 C T A (\lambda (d2: 
+C).(\lambda (u2: T).(\lambda (_: A).(getl i c2 (CHead d2 (Bind Abst) u2))))) 
+(\lambda (d2: C).(\lambda (_: T).(\lambda (_: A).(csuba g d2 d)))) (\lambda 
+(d2: C).(\lambda (u2: T).(\lambda (a1: A).(arity g d2 u2 (asucc g a1))))) 
+(\lambda (_: C).(\lambda (_: T).(\lambda (a1: A).(arity g d u 
+a1)))))).(ex4_3_ind C T A (\lambda (d2: C).(\lambda (u2: T).(\lambda (_: 
+A).(getl i c2 (CHead d2 (Bind Abst) u2))))) (\lambda (d2: C).(\lambda (_: 
+T).(\lambda (_: A).(csuba g d2 d)))) (\lambda (d2: C).(\lambda (u2: 
+T).(\lambda (a1: A).(arity g d2 u2 (asucc g a1))))) (\lambda (_: C).(\lambda 
+(_: T).(\lambda (a1: A).(arity g d u a1)))) (arity g c2 (TLRef i) a0) 
+(\lambda (x0: C).(\lambda (x1: T).(\lambda (x2: A).(\lambda (H7: (getl i c2 
+(CHead x0 (Bind Abst) x1))).(\lambda (_: (csuba g x0 d)).(\lambda (H9: (arity 
+g x0 x1 (asucc g x2))).(\lambda (H10: (arity g d u x2)).(arity_repl g c2 
+(TLRef i) x2 (arity_abst g c2 x0 x1 i H7 x2 H9) a0 (arity_mono g d u x2 H10 
+a0 H1))))))))) H6)) (\lambda (H6: (ex2_2 C T (\lambda (d2: C).(\lambda (u2: 
+T).(getl i c2 (CHead d2 (Bind Void) u2)))) (\lambda (d2: C).(\lambda (_: 
+T).(csuba g d2 d))))).(ex2_2_ind C T (\lambda (d2: C).(\lambda (u2: T).(getl 
+i c2 (CHead d2 (Bind Void) u2)))) (\lambda (d2: C).(\lambda (_: T).(csuba g 
+d2 d))) (arity g c2 (TLRef i) a0) (\lambda (x0: C).(\lambda (x1: T).(\lambda 
+(H7: (getl i c2 (CHead x0 (Bind Void) x1))).(\lambda (_: (csuba g x0 d)).(let 
+H_x0 \def (csubv_getl_conf_void c2 c H4 x0 x1 i H7) in (let H9 \def H_x0 in 
+(ex2_2_ind C T (\lambda (d2: C).(\lambda (_: T).(csubv x0 d2))) (\lambda (d2: 
+C).(\lambda (v2: T).(getl i c (CHead d2 (Bind Void) v2)))) (arity g c2 (TLRef 
+i) a0) (\lambda (x2: C).(\lambda (x3: T).(\lambda (_: (csubv x0 x2)).(\lambda 
+(H11: (getl i c (CHead x2 (Bind Void) x3))).(let H12 \def (eq_ind C (CHead d 
+(Bind Abbr) u) (\lambda (c0: C).(getl i c c0)) H0 (CHead x2 (Bind Void) x3) 
+(getl_mono c (CHead d (Bind Abbr) u) i H0 (CHead x2 (Bind Void) x3) H11)) in 
+(let H13 \def (eq_ind C (CHead d (Bind Abbr) u) (\lambda (ee: C).(match ee 
+with [(CSort _) \Rightarrow False | (CHead _ k _) \Rightarrow (match k with 
+[(Bind b) \Rightarrow (match b with [Abbr \Rightarrow True | Abst \Rightarrow 
+False | Void \Rightarrow False]) | (Flat _) \Rightarrow False])])) I (CHead 
+x2 (Bind Void) x3) (getl_mono c (CHead d (Bind Abbr) u) i H0 (CHead x2 (Bind 
+Void) x3) H11)) in (False_ind (arity g c2 (TLRef i) a0) H13))))))) H9))))))) 
+H6)) H5)))))))))))))) (\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).((csuba g c2 d) \to ((csubv c2 d) \to (arity g c2 u (asucc 
+g a0))))))).(\lambda (c2: C).(\lambda (H3: (csuba g c2 c)).(\lambda (H4: 
+(csubv c2 c)).(let H_x \def (csuba_getl_abst_rev g c d u i H0 c2 H3) in (let 
+H5 \def H_x in (or_ind (ex2 C (\lambda (d2: C).(getl i c2 (CHead d2 (Bind 
+Abst) u))) (\lambda (d2: C).(csuba g d2 d))) (ex2_2 C T (\lambda (d2: 
+C).(\lambda (u2: T).(getl i c2 (CHead d2 (Bind Void) u2)))) (\lambda (d2: 
+C).(\lambda (_: T).(csuba g d2 d)))) (arity g c2 (TLRef i) a0) (\lambda (H6: 
+(ex2 C (\lambda (d2: C).(getl i c2 (CHead d2 (Bind Abst) u))) (\lambda (d2: 
+C).(csuba g d2 d)))).(ex2_ind C (\lambda (d2: C).(getl i c2 (CHead d2 (Bind 
+Abst) u))) (\lambda (d2: C).(csuba g d2 d)) (arity g c2 (TLRef i) a0) 
+(\lambda (x: C).(\lambda (H7: (getl i c2 (CHead x (Bind Abst) u))).(\lambda 
+(H8: (csuba g x d)).(let H_x0 \def (csubv_getl_conf c2 c H4 Abst x u i H7) in 
+(let H9 \def H_x0 in (ex2_3_ind B C T (\lambda (_: B).(\lambda (d2: 
+C).(\lambda (_: T).(csubv x d2)))) (\lambda (b2: B).(\lambda (d2: C).(\lambda 
+(v2: T).(getl i c (CHead d2 (Bind b2) v2))))) (arity g c2 (TLRef i) a0) 
+(\lambda (x0: B).(\lambda (x1: C).(\lambda (x2: T).(\lambda (H10: (csubv x 
+x1)).(\lambda (H11: (getl i c (CHead x1 (Bind x0) x2))).(let H12 \def (eq_ind 
+C (CHead d (Bind Abst) u) (\lambda (c0: C).(getl i c c0)) H0 (CHead x1 (Bind 
+x0) x2) (getl_mono c (CHead d (Bind Abst) u) i H0 (CHead x1 (Bind x0) x2) 
+H11)) in (let H13 \def (f_equal C C (\lambda (e: C).(match e with [(CSort _) 
+\Rightarrow d | (CHead c0 _ _) \Rightarrow c0])) (CHead d (Bind Abst) u) 
 (CHead x1 (Bind x0) x2) (getl_mono c (CHead d (Bind Abst) u) i H0 (CHead x1 
-(Bind x0) x2) H11)) in (let H13 \def (f_equal C C (\lambda (e: C).(match e in 
-C return (\lambda (_: C).C) with [(CSort _) \Rightarrow d | (CHead c0 _ _) 
-\Rightarrow c0])) (CHead d (Bind Abst) u) (CHead x1 (Bind x0) x2) (getl_mono 
-c (CHead d (Bind Abst) u) i H0 (CHead x1 (Bind x0) x2) H11)) in ((let H14 
-\def (f_equal C B (\lambda (e: C).(match e in C return (\lambda (_: C).B) 
-with [(CSort _) \Rightarrow Abst | (CHead _ k _) \Rightarrow (match k in K 
-return (\lambda (_: K).B) with [(Bind b) \Rightarrow b | (Flat _) \Rightarrow 
-Abst])])) (CHead d (Bind Abst) u) (CHead x1 (Bind x0) x2) (getl_mono c (CHead 
-d (Bind Abst) u) i H0 (CHead x1 (Bind x0) x2) H11)) in ((let H15 \def 
-(f_equal C T (\lambda (e: C).(match e in C return (\lambda (_: C).T) with 
-[(CSort _) \Rightarrow u | (CHead _ _ t0) \Rightarrow t0])) (CHead d (Bind 
-Abst) u) (CHead x1 (Bind x0) x2) (getl_mono c (CHead d (Bind Abst) u) i H0 
-(CHead x1 (Bind x0) x2) H11)) in (\lambda (H16: (eq B Abst x0)).(\lambda 
+(Bind x0) x2) H11)) in ((let H14 \def (f_equal C B (\lambda (e: C).(match e 
+with [(CSort _) \Rightarrow Abst | (CHead _ k _) \Rightarrow (match k with 
+[(Bind b) \Rightarrow b | (Flat _) \Rightarrow Abst])])) (CHead d (Bind Abst) 
+u) (CHead x1 (Bind x0) x2) (getl_mono c (CHead d (Bind Abst) u) i H0 (CHead 
+x1 (Bind x0) x2) H11)) in ((let H15 \def (f_equal C T (\lambda (e: C).(match 
+e with [(CSort _) \Rightarrow u | (CHead _ _ t0) \Rightarrow t0])) (CHead d 
+(Bind Abst) u) (CHead x1 (Bind x0) x2) (getl_mono c (CHead d (Bind Abst) u) i 
+H0 (CHead x1 (Bind x0) x2) H11)) in (\lambda (H16: (eq B Abst x0)).(\lambda 
 (H17: (eq C d x1)).(let H18 \def (eq_ind_r T x2 (\lambda (t0: T).(getl i c 
 (CHead x1 (Bind x0) t0))) H12 u H15) in (let H19 \def (eq_ind_r C x1 (\lambda 
 (c0: C).(getl i c (CHead c0 (Bind x0) u))) H18 d H17) in (let H20 \def 
@@ -246,53 +238,48 @@ i) a0) (\lambda (x2: C).(\lambda (x3: T).(\lambda (_: (csubv x0 x2)).(\lambda
 (H11: (getl i c (CHead x2 (Bind Void) x3))).(let H12 \def (eq_ind C (CHead d 
 (Bind Abst) u) (\lambda (c0: C).(getl i c c0)) H0 (CHead x2 (Bind Void) x3) 
 (getl_mono c (CHead d (Bind Abst) u) i H0 (CHead x2 (Bind Void) x3) H11)) in 
-(let H13 \def (eq_ind C (CHead d (Bind Abst) u) (\lambda (ee: C).(match ee in 
-C return (\lambda (_: C).Prop) with [(CSort _) \Rightarrow False | (CHead _ k 
-_) \Rightarrow (match k in K return (\lambda (_: K).Prop) with [(Bind b) 
-\Rightarrow (match b in B return (\lambda (_: B).Prop) with [Abbr \Rightarrow 
-False | Abst \Rightarrow True | Void \Rightarrow False]) | (Flat _) 
-\Rightarrow False])])) I (CHead x2 (Bind Void) x3) (getl_mono c (CHead d 
-(Bind Abst) u) i H0 (CHead x2 (Bind Void) x3) H11)) in (False_ind (arity g c2 
-(TLRef i) a0) H13))))))) H9))))))) H6)) H5)))))))))))))) (\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).((csuba g c2 c) \to ((csubv c2 c) \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).((csuba g c2 (CHead c (Bind b) u)) \to 
-((csubv c2 (CHead c (Bind b) u)) \to (arity g c2 t0 a2)))))).(\lambda (c2: 
-C).(\lambda (H5: (csuba g c2 c)).(\lambda (H6: (csubv c2 c)).(arity_bind g b 
-H0 c2 u a1 (H2 c2 H5 H6) t0 a2 (H4 (CHead c2 (Bind b) u) (csuba_head g c2 c 
-H5 (Bind b) u) (csubv_bind_same c2 c H6 b u u))))))))))))))))) (\lambda (c: 
-C).(\lambda (u: T).(\lambda (a1: A).(\lambda (_: (arity g c u (asucc g 
-a1))).(\lambda (H1: ((\forall (c2: C).((csuba g c2 c) \to ((csubv c2 c) \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).((csuba g c2 (CHead c (Bind Abst) u)) \to ((csubv c2 (CHead c (Bind Abst) 
-u)) \to (arity g c2 t0 a2)))))).(\lambda (c2: C).(\lambda (H4: (csuba g c2 
-c)).(\lambda (H5: (csubv c2 c)).(arity_head g c2 u a1 (H1 c2 H4 H5) t0 a2 (H3 
-(CHead c2 (Bind Abst) u) (csuba_head g c2 c H4 (Bind Abst) u) 
-(csubv_bind_same c2 c H5 Abst u u))))))))))))))) (\lambda (c: C).(\lambda (u: 
-T).(\lambda (a1: A).(\lambda (_: (arity g c u a1)).(\lambda (H1: ((\forall 
-(c2: C).((csuba g c2 c) \to ((csubv c2 c) \to (arity g c2 u a1)))))).(\lambda 
-(t0: T).(\lambda (a2: A).(\lambda (_: (arity g c t0 (AHead a1 a2))).(\lambda 
+(let H13 \def (eq_ind C (CHead d (Bind Abst) u) (\lambda (ee: C).(match ee 
+with [(CSort _) \Rightarrow False | (CHead _ k _) \Rightarrow (match k with 
+[(Bind b) \Rightarrow (match b with [Abbr \Rightarrow False | Abst 
+\Rightarrow True | Void \Rightarrow False]) | (Flat _) \Rightarrow False])])) 
+I (CHead x2 (Bind Void) x3) (getl_mono c (CHead d (Bind Abst) u) i H0 (CHead 
+x2 (Bind Void) x3) H11)) in (False_ind (arity g c2 (TLRef i) a0) H13))))))) 
+H9))))))) H6)) H5)))))))))))))) (\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).((csuba g c2 c) \to ((csubv c2 c) 
+\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).((csuba 
+g c2 (CHead c (Bind b) u)) \to ((csubv c2 (CHead c (Bind b) u)) \to (arity g 
+c2 t0 a2)))))).(\lambda (c2: C).(\lambda (H5: (csuba g c2 c)).(\lambda (H6: 
+(csubv c2 c)).(arity_bind g b H0 c2 u a1 (H2 c2 H5 H6) t0 a2 (H4 (CHead c2 
+(Bind b) u) (csuba_head g c2 c H5 (Bind b) u) (csubv_bind_same c2 c H6 b u 
+u))))))))))))))))) (\lambda (c: C).(\lambda (u: T).(\lambda (a1: A).(\lambda 
+(_: (arity g c u (asucc g a1))).(\lambda (H1: ((\forall (c2: C).((csuba g c2 
+c) \to ((csubv c2 c) \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).((csuba g c2 (CHead c (Bind Abst) u)) 
+\to ((csubv c2 (CHead c (Bind Abst) u)) \to (arity g c2 t0 a2)))))).(\lambda 
+(c2: C).(\lambda (H4: (csuba g c2 c)).(\lambda (H5: (csubv c2 c)).(arity_head 
+g c2 u a1 (H1 c2 H4 H5) t0 a2 (H3 (CHead c2 (Bind Abst) u) (csuba_head g c2 c 
+H4 (Bind Abst) u) (csubv_bind_same c2 c H5 Abst u u))))))))))))))) (\lambda 
+(c: C).(\lambda (u: T).(\lambda (a1: A).(\lambda (_: (arity g c u 
+a1)).(\lambda (H1: ((\forall (c2: C).((csuba g c2 c) \to ((csubv c2 c) \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).((csuba g c2 c) \to 
+((csubv c2 c) \to (arity g c2 t0 (AHead a1 a2))))))).(\lambda (c2: 
+C).(\lambda (H4: (csuba g c2 c)).(\lambda (H5: (csubv c2 c)).(arity_appl g c2 
+u a1 (H1 c2 H4 H5) t0 a2 (H3 c2 H4 H5)))))))))))))) (\lambda (c: C).(\lambda 
+(u: T).(\lambda (a0: A).(\lambda (_: (arity g c u (asucc g a0))).(\lambda 
+(H1: ((\forall (c2: C).((csuba g c2 c) \to ((csubv c2 c) \to (arity g c2 u 
+(asucc g a0))))))).(\lambda (t0: T).(\lambda (_: (arity g c t0 a0)).(\lambda 
 (H3: ((\forall (c2: C).((csuba g c2 c) \to ((csubv c2 c) \to (arity g c2 t0 
-(AHead a1 a2))))))).(\lambda (c2: C).(\lambda (H4: (csuba g c2 c)).(\lambda 
-(H5: (csubv c2 c)).(arity_appl g c2 u a1 (H1 c2 H4 H5) t0 a2 (H3 c2 H4 
-H5)))))))))))))) (\lambda (c: C).(\lambda (u: T).(\lambda (a0: A).(\lambda 
-(_: (arity g c u (asucc g a0))).(\lambda (H1: ((\forall (c2: C).((csuba g c2 
-c) \to ((csubv c2 c) \to (arity g c2 u (asucc g a0))))))).(\lambda (t0: 
-T).(\lambda (_: (arity g c t0 a0)).(\lambda (H3: ((\forall (c2: C).((csuba g 
-c2 c) \to ((csubv c2 c) \to (arity g c2 t0 a0)))))).(\lambda (c2: C).(\lambda 
-(H4: (csuba g c2 c)).(\lambda (H5: (csubv c2 c)).(arity_cast g c2 u a0 (H1 c2 
-H4 H5) t0 (H3 c2 H4 H5))))))))))))) (\lambda (c: C).(\lambda (t0: T).(\lambda 
-(a1: A).(\lambda (_: (arity g c t0 a1)).(\lambda (H1: ((\forall (c2: 
-C).((csuba g c2 c) \to ((csubv c2 c) \to (arity g c2 t0 a1)))))).(\lambda 
-(a2: A).(\lambda (H2: (leq g a1 a2)).(\lambda (c2: C).(\lambda (H3: (csuba g 
-c2 c)).(\lambda (H4: (csubv c2 c)).(arity_repl g c2 t0 a1 (H1 c2 H3 H4) a2 
-H2))))))))))) c1 t a H))))).
-(* COMMENTS
-Initial nodes: 3597
-END *)
+a0)))))).(\lambda (c2: C).(\lambda (H4: (csuba g c2 c)).(\lambda (H5: (csubv 
+c2 c)).(arity_cast g c2 u a0 (H1 c2 H4 H5) t0 (H3 c2 H4 H5))))))))))))) 
+(\lambda (c: C).(\lambda (t0: T).(\lambda (a1: A).(\lambda (_: (arity g c t0 
+a1)).(\lambda (H1: ((\forall (c2: C).((csuba g c2 c) \to ((csubv c2 c) \to 
+(arity g c2 t0 a1)))))).(\lambda (a2: A).(\lambda (H2: (leq g a1 
+a2)).(\lambda (c2: C).(\lambda (H3: (csuba g c2 c)).(\lambda (H4: (csubv c2 
+c)).(arity_repl g c2 t0 a1 (H1 c2 H3 H4) a2 H2))))))))))) c1 t a H))))).
 
 theorem arity_appls_appl:
  \forall (g: G).(\forall (c: C).(\forall (v: T).(\forall (a1: A).((arity g c 
@@ -307,30 +294,26 @@ a1))).(\lambda (t: T).(\lambda (vs: TList).(TList_ind (\lambda (t0:
 TList).(\forall (a2: A).((arity g c (THeads (Flat Appl) t0 (THead (Bind Abbr) 
 v t)) a2) \to (arity g c (THeads (Flat Appl) t0 (THead (Flat Appl) v (THead 
 (Bind Abst) u t))) a2)))) (\lambda (a2: A).(\lambda (H1: (arity g c (THead 
-(Bind Abbr) v t) a2)).(let H_x \def (arity_gen_bind Abbr (\lambda (H2: (eq B 
-Abbr Abst)).(not_abbr_abst H2)) g c v t a2 H1) in (let H2 \def H_x in 
-(ex2_ind A (\lambda (a3: A).(arity g c v a3)) (\lambda (_: A).(arity g (CHead 
-c (Bind Abbr) v) t a2)) (arity g c (THead (Flat Appl) v (THead (Bind Abst) u 
-t)) a2) (\lambda (x: A).(\lambda (_: (arity g c v x)).(\lambda (H4: (arity g 
-(CHead c (Bind Abbr) v) t a2)).(arity_appl g c v a1 H (THead (Bind Abst) u t) 
-a2 (arity_head g c u a1 H0 t a2 (csuba_arity_rev g (CHead c (Bind Abbr) v) t 
-a2 H4 (CHead c (Bind Abst) u) (csuba_abst g c c (csuba_refl g c) u a1 H0 v H) 
-(csubv_bind c c (csubv_refl c) Abst (sym_not_eq B Void Abst not_void_abst) 
-Abbr u v))))))) H2))))) (\lambda (t0: T).(\lambda (t1: TList).(\lambda (H1: 
-((\forall (a2: A).((arity g c (THeads (Flat Appl) t1 (THead (Bind Abbr) v t)) 
-a2) \to (arity g c (THeads (Flat Appl) t1 (THead (Flat Appl) v (THead (Bind 
-Abst) u t))) a2))))).(\lambda (a2: A).(\lambda (H2: (arity g c (THead (Flat 
-Appl) t0 (THeads (Flat Appl) t1 (THead (Bind Abbr) v t))) a2)).(let H3 \def 
-(arity_gen_appl g c t0 (THeads (Flat Appl) t1 (THead (Bind Abbr) v t)) a2 H2) 
-in (ex2_ind A (\lambda (a3: A).(arity g c t0 a3)) (\lambda (a3: A).(arity g c 
-(THeads (Flat Appl) t1 (THead (Bind Abbr) v t)) (AHead a3 a2))) (arity g c 
-(THead (Flat Appl) t0 (THeads (Flat Appl) t1 (THead (Flat Appl) v (THead 
-(Bind Abst) u t)))) a2) (\lambda (x: A).(\lambda (H4: (arity g c t0 
-x)).(\lambda (H5: (arity g c (THeads (Flat Appl) t1 (THead (Bind Abbr) v t)) 
-(AHead x a2))).(arity_appl g c t0 x H4 (THeads (Flat Appl) t1 (THead (Flat 
-Appl) v (THead (Bind Abst) u t))) a2 (H1 (AHead x a2) H5))))) H3))))))) 
-vs))))))))).
-(* COMMENTS
-Initial nodes: 687
-END *)
+(Bind Abbr) v t) a2)).(let H_x \def (arity_gen_bind Abbr not_abbr_abst g c v 
+t a2 H1) in (let H2 \def H_x in (ex2_ind A (\lambda (a3: A).(arity g c v a3)) 
+(\lambda (_: A).(arity g (CHead c (Bind Abbr) v) t a2)) (arity g c (THead 
+(Flat Appl) v (THead (Bind Abst) u t)) a2) (\lambda (x: A).(\lambda (_: 
+(arity g c v x)).(\lambda (H4: (arity g (CHead c (Bind Abbr) v) t 
+a2)).(arity_appl g c v a1 H (THead (Bind Abst) u t) a2 (arity_head g c u a1 
+H0 t a2 (csuba_arity_rev g (CHead c (Bind Abbr) v) t a2 H4 (CHead c (Bind 
+Abst) u) (csuba_abst g c c (csuba_refl g c) u a1 H0 v H) (csubv_bind c c 
+(csubv_refl c) Abst not_abst_void Abbr u v))))))) H2))))) (\lambda (t0: 
+T).(\lambda (t1: TList).(\lambda (H1: ((\forall (a2: A).((arity g c (THeads 
+(Flat Appl) t1 (THead (Bind Abbr) v t)) a2) \to (arity g c (THeads (Flat 
+Appl) t1 (THead (Flat Appl) v (THead (Bind Abst) u t))) a2))))).(\lambda (a2: 
+A).(\lambda (H2: (arity g c (THead (Flat Appl) t0 (THeads (Flat Appl) t1 
+(THead (Bind Abbr) v t))) a2)).(let H3 \def (arity_gen_appl g c t0 (THeads 
+(Flat Appl) t1 (THead (Bind Abbr) v t)) a2 H2) in (ex2_ind A (\lambda (a3: 
+A).(arity g c t0 a3)) (\lambda (a3: A).(arity g c (THeads (Flat Appl) t1 
+(THead (Bind Abbr) v t)) (AHead a3 a2))) (arity g c (THead (Flat Appl) t0 
+(THeads (Flat Appl) t1 (THead (Flat Appl) v (THead (Bind Abst) u t)))) a2) 
+(\lambda (x: A).(\lambda (H4: (arity g c t0 x)).(\lambda (H5: (arity g c 
+(THeads (Flat Appl) t1 (THead (Bind Abbr) v t)) (AHead x a2))).(arity_appl g 
+c t0 x H4 (THeads (Flat Appl) t1 (THead (Flat Appl) v (THead (Bind Abst) u 
+t))) a2 (H1 (AHead x a2) H5))))) H3))))))) vs))))))))).