X-Git-Url: http://matita.cs.unibo.it/gitweb/?a=blobdiff_plain;f=helm%2Fsoftware%2Fmatita%2Fcontribs%2FLAMBDA-TYPES%2FLambdaDelta-1%2Fcsubst0%2Ffwd.ma;h=3052659c06ae523120cea0ceaf48e73bbbe72b3e;hb=89519c7b52e06304a94019dd528925300380cdc0;hp=585127337c1d3545aec6c504b5232a7b0b075117;hpb=863c1f7bb313c3d9dff08d60c8c7ef7c511263c4;p=helm.git

diff --git a/helm/software/matita/contribs/LAMBDA-TYPES/LambdaDelta-1/csubst0/fwd.ma b/helm/software/matita/contribs/LAMBDA-TYPES/LambdaDelta-1/csubst0/fwd.ma
index 585127337..3052659c0 100644
--- a/helm/software/matita/contribs/LAMBDA-TYPES/LambdaDelta-1/csubst0/fwd.ma
+++ b/helm/software/matita/contribs/LAMBDA-TYPES/LambdaDelta-1/csubst0/fwd.ma
@@ -261,3 +261,193 @@ u3)))) (\lambda (_: T).(\lambda (c3: C).(\lambda (j: nat).(csubst0 j v0 c1
 c3)))) u2 c2 i0 (refl_equal nat (s k i0)) (refl_equal C (CHead c2 k u2)) H12 
 H11)) k0 H8))))))) H6)) H5))))))))))))) i v y x H0))) H))))))).
 
+theorem csubst0_gen_S_bind_2:
+ \forall (b: B).(\forall (x: C).(\forall (c2: C).(\forall (v: T).(\forall 
+(v2: T).(\forall (i: nat).((csubst0 (S i) v x (CHead c2 (Bind b) v2)) \to 
+(or3 (ex2 T (\lambda (v1: T).(subst0 i v v1 v2)) (\lambda (v1: T).(eq C x 
+(CHead c2 (Bind b) v1)))) (ex2 C (\lambda (c1: C).(csubst0 i v c1 c2)) 
+(\lambda (c1: C).(eq C x (CHead c1 (Bind b) v2)))) (ex3_2 C T (\lambda (_: 
+C).(\lambda (v1: T).(subst0 i v v1 v2))) (\lambda (c1: C).(\lambda (_: 
+T).(csubst0 i v c1 c2))) (\lambda (c1: C).(\lambda (v1: T).(eq C x (CHead c1 
+(Bind b) v1))))))))))))
+\def
+ \lambda (b: B).(\lambda (x: C).(\lambda (c2: C).(\lambda (v: T).(\lambda 
+(v2: T).(\lambda (i: nat).(\lambda (H: (csubst0 (S i) v x (CHead c2 (Bind b) 
+v2))).(insert_eq C (CHead c2 (Bind b) v2) (\lambda (c: C).(csubst0 (S i) v x 
+c)) (\lambda (_: C).(or3 (ex2 T (\lambda (v1: T).(subst0 i v v1 v2)) (\lambda 
+(v1: T).(eq C x (CHead c2 (Bind b) v1)))) (ex2 C (\lambda (c1: C).(csubst0 i 
+v c1 c2)) (\lambda (c1: C).(eq C x (CHead c1 (Bind b) v2)))) (ex3_2 C T 
+(\lambda (_: C).(\lambda (v1: T).(subst0 i v v1 v2))) (\lambda (c1: 
+C).(\lambda (_: T).(csubst0 i v c1 c2))) (\lambda (c1: C).(\lambda (v1: 
+T).(eq C x (CHead c1 (Bind b) v1))))))) (\lambda (y: C).(\lambda (H0: 
+(csubst0 (S i) v x y)).(insert_eq nat (S i) (\lambda (n: nat).(csubst0 n v x 
+y)) (\lambda (_: nat).((eq C y (CHead c2 (Bind b) v2)) \to (or3 (ex2 T 
+(\lambda (v1: T).(subst0 i v v1 v2)) (\lambda (v1: T).(eq C x (CHead c2 (Bind 
+b) v1)))) (ex2 C (\lambda (c1: C).(csubst0 i v c1 c2)) (\lambda (c1: C).(eq C 
+x (CHead c1 (Bind b) v2)))) (ex3_2 C T (\lambda (_: C).(\lambda (v1: 
+T).(subst0 i v v1 v2))) (\lambda (c1: C).(\lambda (_: T).(csubst0 i v c1 
+c2))) (\lambda (c1: C).(\lambda (v1: T).(eq C x (CHead c1 (Bind b) v1)))))))) 
+(\lambda (y0: nat).(\lambda (H1: (csubst0 y0 v x y)).(csubst0_ind (\lambda 
+(n: nat).(\lambda (t: T).(\lambda (c: C).(\lambda (c0: C).((eq nat n (S i)) 
+\to ((eq C c0 (CHead c2 (Bind b) v2)) \to (or3 (ex2 T (\lambda (v1: 
+T).(subst0 i t v1 v2)) (\lambda (v1: T).(eq C c (CHead c2 (Bind b) v1)))) 
+(ex2 C (\lambda (c1: C).(csubst0 i t c1 c2)) (\lambda (c1: C).(eq C c (CHead 
+c1 (Bind b) v2)))) (ex3_2 C T (\lambda (_: C).(\lambda (v1: T).(subst0 i t v1 
+v2))) (\lambda (c1: C).(\lambda (_: T).(csubst0 i t c1 c2))) (\lambda (c1: 
+C).(\lambda (v1: T).(eq C c (CHead c1 (Bind b) v1)))))))))))) (\lambda (k: 
+K).(\lambda (i0: nat).(\lambda (v0: T).(\lambda (u1: T).(\lambda (u2: 
+T).(\lambda (H2: (subst0 i0 v0 u1 u2)).(\lambda (c: C).(\lambda (H3: (eq nat 
+(s k i0) (S i))).(\lambda (H4: (eq C (CHead c k u2) (CHead c2 (Bind b) 
+v2))).(let H5 \def (f_equal C C (\lambda (e: C).(match e in C return (\lambda 
+(_: C).C) with [(CSort _) \Rightarrow c | (CHead c0 _ _) \Rightarrow c0])) 
+(CHead c k u2) (CHead c2 (Bind b) v2) H4) in ((let H6 \def (f_equal C K 
+(\lambda (e: C).(match e in C return (\lambda (_: C).K) with [(CSort _) 
+\Rightarrow k | (CHead _ k0 _) \Rightarrow k0])) (CHead c k u2) (CHead c2 
+(Bind b) v2) H4) in ((let H7 \def (f_equal C T (\lambda (e: C).(match e in C 
+return (\lambda (_: C).T) with [(CSort _) \Rightarrow u2 | (CHead _ _ t) 
+\Rightarrow t])) (CHead c k u2) (CHead c2 (Bind b) v2) H4) in (\lambda (H8: 
+(eq K k (Bind b))).(\lambda (H9: (eq C c c2)).(eq_ind_r C c2 (\lambda (c0: 
+C).(or3 (ex2 T (\lambda (v1: T).(subst0 i v0 v1 v2)) (\lambda (v1: T).(eq C 
+(CHead c0 k u1) (CHead c2 (Bind b) v1)))) (ex2 C (\lambda (c1: C).(csubst0 i 
+v0 c1 c2)) (\lambda (c1: C).(eq C (CHead c0 k u1) (CHead c1 (Bind b) v2)))) 
+(ex3_2 C T (\lambda (_: C).(\lambda (v1: T).(subst0 i v0 v1 v2))) (\lambda 
+(c1: C).(\lambda (_: T).(csubst0 i v0 c1 c2))) (\lambda (c1: C).(\lambda (v1: 
+T).(eq C (CHead c0 k u1) (CHead c1 (Bind b) v1))))))) (let H10 \def (eq_ind T 
+u2 (\lambda (t: T).(subst0 i0 v0 u1 t)) H2 v2 H7) in (let H11 \def (eq_ind K 
+k (\lambda (k0: K).(eq nat (s k0 i0) (S i))) H3 (Bind b) H8) in (eq_ind_r K 
+(Bind b) (\lambda (k0: K).(or3 (ex2 T (\lambda (v1: T).(subst0 i v0 v1 v2)) 
+(\lambda (v1: T).(eq C (CHead c2 k0 u1) (CHead c2 (Bind b) v1)))) (ex2 C 
+(\lambda (c1: C).(csubst0 i v0 c1 c2)) (\lambda (c1: C).(eq C (CHead c2 k0 
+u1) (CHead c1 (Bind b) v2)))) (ex3_2 C T (\lambda (_: C).(\lambda (v1: 
+T).(subst0 i v0 v1 v2))) (\lambda (c1: C).(\lambda (_: T).(csubst0 i v0 c1 
+c2))) (\lambda (c1: C).(\lambda (v1: T).(eq C (CHead c2 k0 u1) (CHead c1 
+(Bind b) v1))))))) (let H12 \def (f_equal nat nat (\lambda (e: nat).(match e 
+in nat return (\lambda (_: nat).nat) with [O \Rightarrow i0 | (S n) 
+\Rightarrow n])) (S i0) (S i) H11) in (let H13 \def (eq_ind nat i0 (\lambda 
+(n: nat).(subst0 n v0 u1 v2)) H10 i H12) in (or3_intro0 (ex2 T (\lambda (v1: 
+T).(subst0 i v0 v1 v2)) (\lambda (v1: T).(eq C (CHead c2 (Bind b) u1) (CHead 
+c2 (Bind b) v1)))) (ex2 C (\lambda (c1: C).(csubst0 i v0 c1 c2)) (\lambda 
+(c1: C).(eq C (CHead c2 (Bind b) u1) (CHead c1 (Bind b) v2)))) (ex3_2 C T 
+(\lambda (_: C).(\lambda (v1: T).(subst0 i v0 v1 v2))) (\lambda (c1: 
+C).(\lambda (_: T).(csubst0 i v0 c1 c2))) (\lambda (c1: C).(\lambda (v1: 
+T).(eq C (CHead c2 (Bind b) u1) (CHead c1 (Bind b) v1))))) (ex_intro2 T 
+(\lambda (v1: T).(subst0 i v0 v1 v2)) (\lambda (v1: T).(eq C (CHead c2 (Bind 
+b) u1) (CHead c2 (Bind b) v1))) u1 H13 (refl_equal C (CHead c2 (Bind b) 
+u1)))))) k H8))) c H9)))) H6)) H5))))))))))) (\lambda (k: K).(\lambda (i0: 
+nat).(\lambda (c1: C).(\lambda (c0: C).(\lambda (v0: T).(\lambda (H2: 
+(csubst0 i0 v0 c1 c0)).(\lambda (H3: (((eq nat i0 (S i)) \to ((eq C c0 (CHead 
+c2 (Bind b) v2)) \to (or3 (ex2 T (\lambda (v1: T).(subst0 i v0 v1 v2)) 
+(\lambda (v1: T).(eq C c1 (CHead c2 (Bind b) v1)))) (ex2 C (\lambda (c3: 
+C).(csubst0 i v0 c3 c2)) (\lambda (c3: C).(eq C c1 (CHead c3 (Bind b) v2)))) 
+(ex3_2 C T (\lambda (_: C).(\lambda (v1: T).(subst0 i v0 v1 v2))) (\lambda 
+(c3: C).(\lambda (_: T).(csubst0 i v0 c3 c2))) (\lambda (c3: C).(\lambda (v1: 
+T).(eq C c1 (CHead c3 (Bind b) v1)))))))))).(\lambda (u: T).(\lambda (H4: (eq 
+nat (s k i0) (S i))).(\lambda (H5: (eq C (CHead c0 k u) (CHead c2 (Bind b) 
+v2))).(let H6 \def (f_equal C C (\lambda (e: C).(match e in C return (\lambda 
+(_: C).C) with [(CSort _) \Rightarrow c0 | (CHead c _ _) \Rightarrow c])) 
+(CHead c0 k u) (CHead c2 (Bind b) v2) H5) in ((let H7 \def (f_equal C K 
+(\lambda (e: C).(match e in C return (\lambda (_: C).K) with [(CSort _) 
+\Rightarrow k | (CHead _ k0 _) \Rightarrow k0])) (CHead c0 k u) (CHead c2 
+(Bind b) v2) H5) in ((let H8 \def (f_equal C T (\lambda (e: C).(match e in C 
+return (\lambda (_: C).T) with [(CSort _) \Rightarrow u | (CHead _ _ t) 
+\Rightarrow t])) (CHead c0 k u) (CHead c2 (Bind b) v2) H5) in (\lambda (H9: 
+(eq K k (Bind b))).(\lambda (H10: (eq C c0 c2)).(eq_ind_r T v2 (\lambda (t: 
+T).(or3 (ex2 T (\lambda (v1: T).(subst0 i v0 v1 v2)) (\lambda (v1: T).(eq C 
+(CHead c1 k t) (CHead c2 (Bind b) v1)))) (ex2 C (\lambda (c3: C).(csubst0 i 
+v0 c3 c2)) (\lambda (c3: C).(eq C (CHead c1 k t) (CHead c3 (Bind b) v2)))) 
+(ex3_2 C T (\lambda (_: C).(\lambda (v1: T).(subst0 i v0 v1 v2))) (\lambda 
+(c3: C).(\lambda (_: T).(csubst0 i v0 c3 c2))) (\lambda (c3: C).(\lambda (v1: 
+T).(eq C (CHead c1 k t) (CHead c3 (Bind b) v1))))))) (let H11 \def (eq_ind C 
+c0 (\lambda (c: C).((eq nat i0 (S i)) \to ((eq C c (CHead c2 (Bind b) v2)) 
+\to (or3 (ex2 T (\lambda (v1: T).(subst0 i v0 v1 v2)) (\lambda (v1: T).(eq C 
+c1 (CHead c2 (Bind b) v1)))) (ex2 C (\lambda (c3: C).(csubst0 i v0 c3 c2)) 
+(\lambda (c3: C).(eq C c1 (CHead c3 (Bind b) v2)))) (ex3_2 C T (\lambda (_: 
+C).(\lambda (v1: T).(subst0 i v0 v1 v2))) (\lambda (c3: C).(\lambda (_: 
+T).(csubst0 i v0 c3 c2))) (\lambda (c3: C).(\lambda (v1: T).(eq C c1 (CHead 
+c3 (Bind b) v1))))))))) H3 c2 H10) in (let H12 \def (eq_ind C c0 (\lambda (c: 
+C).(csubst0 i0 v0 c1 c)) H2 c2 H10) in (let H13 \def (eq_ind K k (\lambda 
+(k0: K).(eq nat (s k0 i0) (S i))) H4 (Bind b) H9) in (eq_ind_r K (Bind b) 
+(\lambda (k0: K).(or3 (ex2 T (\lambda (v1: T).(subst0 i v0 v1 v2)) (\lambda 
+(v1: T).(eq C (CHead c1 k0 v2) (CHead c2 (Bind b) v1)))) (ex2 C (\lambda (c3: 
+C).(csubst0 i v0 c3 c2)) (\lambda (c3: C).(eq C (CHead c1 k0 v2) (CHead c3 
+(Bind b) v2)))) (ex3_2 C T (\lambda (_: C).(\lambda (v1: T).(subst0 i v0 v1 
+v2))) (\lambda (c3: C).(\lambda (_: T).(csubst0 i v0 c3 c2))) (\lambda (c3: 
+C).(\lambda (v1: T).(eq C (CHead c1 k0 v2) (CHead c3 (Bind b) v1))))))) (let 
+H14 \def (f_equal nat nat (\lambda (e: nat).(match e in nat return (\lambda 
+(_: nat).nat) with [O \Rightarrow i0 | (S n) \Rightarrow n])) (S i0) (S i) 
+H13) in (let H15 \def (eq_ind nat i0 (\lambda (n: nat).((eq nat n (S i)) \to 
+((eq C c2 (CHead c2 (Bind b) v2)) \to (or3 (ex2 T (\lambda (v1: T).(subst0 i 
+v0 v1 v2)) (\lambda (v1: T).(eq C c1 (CHead c2 (Bind b) v1)))) (ex2 C 
+(\lambda (c3: C).(csubst0 i v0 c3 c2)) (\lambda (c3: C).(eq C c1 (CHead c3 
+(Bind b) v2)))) (ex3_2 C T (\lambda (_: C).(\lambda (v1: T).(subst0 i v0 v1 
+v2))) (\lambda (c3: C).(\lambda (_: T).(csubst0 i v0 c3 c2))) (\lambda (c3: 
+C).(\lambda (v1: T).(eq C c1 (CHead c3 (Bind b) v1))))))))) H11 i H14) in 
+(let H16 \def (eq_ind nat i0 (\lambda (n: nat).(csubst0 n v0 c1 c2)) H12 i 
+H14) in (or3_intro1 (ex2 T (\lambda (v1: T).(subst0 i v0 v1 v2)) (\lambda 
+(v1: T).(eq C (CHead c1 (Bind b) v2) (CHead c2 (Bind b) v1)))) (ex2 C 
+(\lambda (c3: C).(csubst0 i v0 c3 c2)) (\lambda (c3: C).(eq C (CHead c1 (Bind 
+b) v2) (CHead c3 (Bind b) v2)))) (ex3_2 C T (\lambda (_: C).(\lambda (v1: 
+T).(subst0 i v0 v1 v2))) (\lambda (c3: C).(\lambda (_: T).(csubst0 i v0 c3 
+c2))) (\lambda (c3: C).(\lambda (v1: T).(eq C (CHead c1 (Bind b) v2) (CHead 
+c3 (Bind b) v1))))) (ex_intro2 C (\lambda (c3: C).(csubst0 i v0 c3 c2)) 
+(\lambda (c3: C).(eq C (CHead c1 (Bind b) v2) (CHead c3 (Bind b) v2))) c1 H16 
+(refl_equal C (CHead c1 (Bind b) v2))))))) k H9)))) u H8)))) H7)) 
+H6)))))))))))) (\lambda (k: K).(\lambda (i0: nat).(\lambda (v0: T).(\lambda 
+(u1: T).(\lambda (u2: T).(\lambda (H2: (subst0 i0 v0 u1 u2)).(\lambda (c1: 
+C).(\lambda (c0: C).(\lambda (H3: (csubst0 i0 v0 c1 c0)).(\lambda (H4: (((eq 
+nat i0 (S i)) \to ((eq C c0 (CHead c2 (Bind b) v2)) \to (or3 (ex2 T (\lambda 
+(v1: T).(subst0 i v0 v1 v2)) (\lambda (v1: T).(eq C c1 (CHead c2 (Bind b) 
+v1)))) (ex2 C (\lambda (c3: C).(csubst0 i v0 c3 c2)) (\lambda (c3: C).(eq C 
+c1 (CHead c3 (Bind b) v2)))) (ex3_2 C T (\lambda (_: C).(\lambda (v1: 
+T).(subst0 i v0 v1 v2))) (\lambda (c3: C).(\lambda (_: T).(csubst0 i v0 c3 
+c2))) (\lambda (c3: C).(\lambda (v1: T).(eq C c1 (CHead c3 (Bind b) 
+v1)))))))))).(\lambda (H5: (eq nat (s k i0) (S i))).(\lambda (H6: (eq C 
+(CHead c0 k u2) (CHead c2 (Bind b) v2))).(let H7 \def (f_equal C C (\lambda 
+(e: C).(match e in C return (\lambda (_: C).C) with [(CSort _) \Rightarrow c0 
+| (CHead c _ _) \Rightarrow c])) (CHead c0 k u2) (CHead c2 (Bind b) v2) H6) 
+in ((let H8 \def (f_equal C K (\lambda (e: C).(match e in C return (\lambda 
+(_: C).K) with [(CSort _) \Rightarrow k | (CHead _ k0 _) \Rightarrow k0])) 
+(CHead c0 k u2) (CHead c2 (Bind b) v2) H6) in ((let H9 \def (f_equal C T 
+(\lambda (e: C).(match e in C return (\lambda (_: C).T) with [(CSort _) 
+\Rightarrow u2 | (CHead _ _ t) \Rightarrow t])) (CHead c0 k u2) (CHead c2 
+(Bind b) v2) H6) in (\lambda (H10: (eq K k (Bind b))).(\lambda (H11: (eq C c0 
+c2)).(let H12 \def (eq_ind C c0 (\lambda (c: C).((eq nat i0 (S i)) \to ((eq C 
+c (CHead c2 (Bind b) v2)) \to (or3 (ex2 T (\lambda (v1: T).(subst0 i v0 v1 
+v2)) (\lambda (v1: T).(eq C c1 (CHead c2 (Bind b) v1)))) (ex2 C (\lambda (c3: 
+C).(csubst0 i v0 c3 c2)) (\lambda (c3: C).(eq C c1 (CHead c3 (Bind b) v2)))) 
+(ex3_2 C T (\lambda (_: C).(\lambda (v1: T).(subst0 i v0 v1 v2))) (\lambda 
+(c3: C).(\lambda (_: T).(csubst0 i v0 c3 c2))) (\lambda (c3: C).(\lambda (v1: 
+T).(eq C c1 (CHead c3 (Bind b) v1))))))))) H4 c2 H11) in (let H13 \def 
+(eq_ind C c0 (\lambda (c: C).(csubst0 i0 v0 c1 c)) H3 c2 H11) in (let H14 
+\def (eq_ind T u2 (\lambda (t: T).(subst0 i0 v0 u1 t)) H2 v2 H9) in (let H15 
+\def (eq_ind K k (\lambda (k0: K).(eq nat (s k0 i0) (S i))) H5 (Bind b) H10) 
+in (eq_ind_r K (Bind b) (\lambda (k0: K).(or3 (ex2 T (\lambda (v1: T).(subst0 
+i v0 v1 v2)) (\lambda (v1: T).(eq C (CHead c1 k0 u1) (CHead c2 (Bind b) 
+v1)))) (ex2 C (\lambda (c3: C).(csubst0 i v0 c3 c2)) (\lambda (c3: C).(eq C 
+(CHead c1 k0 u1) (CHead c3 (Bind b) v2)))) (ex3_2 C T (\lambda (_: 
+C).(\lambda (v1: T).(subst0 i v0 v1 v2))) (\lambda (c3: C).(\lambda (_: 
+T).(csubst0 i v0 c3 c2))) (\lambda (c3: C).(\lambda (v1: T).(eq C (CHead c1 
+k0 u1) (CHead c3 (Bind b) v1))))))) (let H16 \def (f_equal nat nat (\lambda 
+(e: nat).(match e in nat return (\lambda (_: nat).nat) with [O \Rightarrow i0 
+| (S n) \Rightarrow n])) (S i0) (S i) H15) in (let H17 \def (eq_ind nat i0 
+(\lambda (n: nat).((eq nat n (S i)) \to ((eq C c2 (CHead c2 (Bind b) v2)) \to 
+(or3 (ex2 T (\lambda (v1: T).(subst0 i v0 v1 v2)) (\lambda (v1: T).(eq C c1 
+(CHead c2 (Bind b) v1)))) (ex2 C (\lambda (c3: C).(csubst0 i v0 c3 c2)) 
+(\lambda (c3: C).(eq C c1 (CHead c3 (Bind b) v2)))) (ex3_2 C T (\lambda (_: 
+C).(\lambda (v1: T).(subst0 i v0 v1 v2))) (\lambda (c3: C).(\lambda (_: 
+T).(csubst0 i v0 c3 c2))) (\lambda (c3: C).(\lambda (v1: T).(eq C c1 (CHead 
+c3 (Bind b) v1))))))))) H12 i H16) in (let H18 \def (eq_ind nat i0 (\lambda 
+(n: nat).(csubst0 n v0 c1 c2)) H13 i H16) in (let H19 \def (eq_ind nat i0 
+(\lambda (n: nat).(subst0 n v0 u1 v2)) H14 i H16) in (or3_intro2 (ex2 T 
+(\lambda (v1: T).(subst0 i v0 v1 v2)) (\lambda (v1: T).(eq C (CHead c1 (Bind 
+b) u1) (CHead c2 (Bind b) v1)))) (ex2 C (\lambda (c3: C).(csubst0 i v0 c3 
+c2)) (\lambda (c3: C).(eq C (CHead c1 (Bind b) u1) (CHead c3 (Bind b) v2)))) 
+(ex3_2 C T (\lambda (_: C).(\lambda (v1: T).(subst0 i v0 v1 v2))) (\lambda 
+(c3: C).(\lambda (_: T).(csubst0 i v0 c3 c2))) (\lambda (c3: C).(\lambda (v1: 
+T).(eq C (CHead c1 (Bind b) u1) (CHead c3 (Bind b) v1))))) (ex3_2_intro C T 
+(\lambda (_: C).(\lambda (v1: T).(subst0 i v0 v1 v2))) (\lambda (c3: 
+C).(\lambda (_: T).(csubst0 i v0 c3 c2))) (\lambda (c3: C).(\lambda (v1: 
+T).(eq C (CHead c1 (Bind b) u1) (CHead c3 (Bind b) v1)))) c1 u1 H19 H18 
+(refl_equal C (CHead c1 (Bind b) u1)))))))) k H10)))))))) H8)) 
+H7)))))))))))))) y0 v x y H1))) H0))) H))))))).
+