c2) \to (ex2 C (\lambda (e2: C).(drop n O c2 e2)) (\lambda (e2: C).(csubc g
e1 e2)))))))).(\lambda (H1: (drop (S n) O (CHead c k t) e1)).(\lambda (c2:
C).(\lambda (H2: (csubc g (CHead c k t) c2)).(let H_x \def (csubc_gen_head_l
-g c c2 t k H2) in (let H3 \def H_x in (or_ind (ex2 C (\lambda (c3: C).(eq C
+g c c2 t k H2) in (let H3 \def H_x in (or3_ind (ex2 C (\lambda (c3: C).(eq C
c2 (CHead c3 k t))) (\lambda (c3: C).(csubc g c c3))) (ex5_3 C T A (\lambda
(_: C).(\lambda (_: T).(\lambda (_: A).(eq K k (Bind Abst))))) (\lambda (c3:
C).(\lambda (w: T).(\lambda (_: A).(eq C c2 (CHead c3 (Bind Abbr) w)))))
(\lambda (c3: C).(\lambda (_: T).(\lambda (_: A).(csubc g c c3)))) (\lambda
(_: C).(\lambda (_: T).(\lambda (a: A).(sc3 g (asucc g a) c t)))) (\lambda
-(c3: C).(\lambda (w: T).(\lambda (a: A).(sc3 g a c3 w))))) (ex2 C (\lambda
-(e2: C).(drop (S n) O c2 e2)) (\lambda (e2: C).(csubc g e1 e2))) (\lambda
-(H4: (ex2 C (\lambda (c3: C).(eq C c2 (CHead c3 k t))) (\lambda (c3:
-C).(csubc g c c3)))).(ex2_ind C (\lambda (c3: C).(eq C c2 (CHead c3 k t)))
-(\lambda (c3: C).(csubc g c c3)) (ex2 C (\lambda (e2: C).(drop (S n) O c2
-e2)) (\lambda (e2: C).(csubc g e1 e2))) (\lambda (x: C).(\lambda (H5: (eq C
-c2 (CHead x k t))).(\lambda (H6: (csubc g c x)).(eq_ind_r C (CHead x k t)
-(\lambda (c0: C).(ex2 C (\lambda (e2: C).(drop (S n) O c0 e2)) (\lambda (e2:
-C).(csubc g e1 e2)))) (let H_x0 \def (H e1 (r k n) (drop_gen_drop k c e1 t n
-H1) x H6) in (let H7 \def H_x0 in (ex2_ind C (\lambda (e2: C).(drop (r k n) O
-x e2)) (\lambda (e2: C).(csubc g e1 e2)) (ex2 C (\lambda (e2: C).(drop (S n)
-O (CHead x k t) e2)) (\lambda (e2: C).(csubc g e1 e2))) (\lambda (x0:
-C).(\lambda (H8: (drop (r k n) O x x0)).(\lambda (H9: (csubc g e1
-x0)).(ex_intro2 C (\lambda (e2: C).(drop (S n) O (CHead x k t) e2)) (\lambda
-(e2: C).(csubc g e1 e2)) x0 (drop_drop k n x x0 H8 t) H9)))) H7))) c2 H5))))
-H4)) (\lambda (H4: (ex5_3 C T A (\lambda (_: C).(\lambda (_: T).(\lambda (_:
-A).(eq K k (Bind Abst))))) (\lambda (c3: C).(\lambda (w: T).(\lambda (_:
-A).(eq C c2 (CHead c3 (Bind Abbr) w))))) (\lambda (c3: C).(\lambda (_:
-T).(\lambda (_: A).(csubc g c c3)))) (\lambda (_: C).(\lambda (_: T).(\lambda
-(a: A).(sc3 g (asucc g a) c t)))) (\lambda (c3: C).(\lambda (w: T).(\lambda
-(a: A).(sc3 g a c3 w)))))).(ex5_3_ind C T A (\lambda (_: C).(\lambda (_:
-T).(\lambda (_: A).(eq K k (Bind Abst))))) (\lambda (c3: C).(\lambda (w:
-T).(\lambda (_: A).(eq C c2 (CHead c3 (Bind Abbr) w))))) (\lambda (c3:
-C).(\lambda (_: T).(\lambda (_: A).(csubc g c c3)))) (\lambda (_: C).(\lambda
-(_: T).(\lambda (a: A).(sc3 g (asucc g a) c t)))) (\lambda (c3: C).(\lambda
-(w: T).(\lambda (a: A).(sc3 g a c3 w)))) (ex2 C (\lambda (e2: C).(drop (S n)
-O c2 e2)) (\lambda (e2: C).(csubc g e1 e2))) (\lambda (x0: C).(\lambda (x1:
-T).(\lambda (x2: A).(\lambda (H5: (eq K k (Bind Abst))).(\lambda (H6: (eq C
-c2 (CHead x0 (Bind Abbr) x1))).(\lambda (H7: (csubc g c x0)).(\lambda (_:
-(sc3 g (asucc g x2) c t)).(\lambda (_: (sc3 g x2 x0 x1)).(eq_ind_r C (CHead
-x0 (Bind Abbr) x1) (\lambda (c0: C).(ex2 C (\lambda (e2: C).(drop (S n) O c0
-e2)) (\lambda (e2: C).(csubc g e1 e2)))) (let H10 \def (eq_ind K k (\lambda
-(k0: K).(drop (r k0 n) O c e1)) (drop_gen_drop k c e1 t n H1) (Bind Abst) H5)
-in (let H11 \def (eq_ind K k (\lambda (k0: K).((drop n O (CHead c k0 t) e1)
-\to (\forall (c3: C).((csubc g (CHead c k0 t) c3) \to (ex2 C (\lambda (e2:
-C).(drop n O c3 e2)) (\lambda (e2: C).(csubc g e1 e2))))))) H0 (Bind Abst)
-H5) in (let H_x0 \def (H e1 (r (Bind Abst) n) H10 x0 H7) in (let H12 \def
-H_x0 in (ex2_ind C (\lambda (e2: C).(drop n O x0 e2)) (\lambda (e2: C).(csubc
-g e1 e2)) (ex2 C (\lambda (e2: C).(drop (S n) O (CHead x0 (Bind Abbr) x1)
-e2)) (\lambda (e2: C).(csubc g e1 e2))) (\lambda (x: C).(\lambda (H13: (drop
-n O x0 x)).(\lambda (H14: (csubc g e1 x)).(ex_intro2 C (\lambda (e2: C).(drop
-(S n) O (CHead x0 (Bind Abbr) x1) e2)) (\lambda (e2: C).(csubc g e1 e2)) x
-(drop_drop (Bind Abbr) n x0 x H13 x1) H14)))) H12))))) c2 H6))))))))) H4))
-H3)))))))) h))))))) c1)).
+(c3: C).(\lambda (w: T).(\lambda (a: A).(sc3 g a c3 w))))) (ex4_3 B C T
+(\lambda (b: B).(\lambda (c3: C).(\lambda (v2: T).(eq C c2 (CHead c3 (Bind b)
+v2))))) (\lambda (_: B).(\lambda (_: C).(\lambda (_: T).(eq K k (Bind
+Void))))) (\lambda (b: B).(\lambda (_: C).(\lambda (_: T).(not (eq B b
+Void))))) (\lambda (_: B).(\lambda (c3: C).(\lambda (_: T).(csubc g c c3)))))
+(ex2 C (\lambda (e2: C).(drop (S n) O c2 e2)) (\lambda (e2: C).(csubc g e1
+e2))) (\lambda (H4: (ex2 C (\lambda (c3: C).(eq C c2 (CHead c3 k t)))
+(\lambda (c3: C).(csubc g c c3)))).(ex2_ind C (\lambda (c3: C).(eq C c2
+(CHead c3 k t))) (\lambda (c3: C).(csubc g c c3)) (ex2 C (\lambda (e2:
+C).(drop (S n) O c2 e2)) (\lambda (e2: C).(csubc g e1 e2))) (\lambda (x:
+C).(\lambda (H5: (eq C c2 (CHead x k t))).(\lambda (H6: (csubc g c
+x)).(eq_ind_r C (CHead x k t) (\lambda (c0: C).(ex2 C (\lambda (e2: C).(drop
+(S n) O c0 e2)) (\lambda (e2: C).(csubc g e1 e2)))) (let H_x0 \def (H e1 (r k
+n) (drop_gen_drop k c e1 t n H1) x H6) in (let H7 \def H_x0 in (ex2_ind C
+(\lambda (e2: C).(drop (r k n) O x e2)) (\lambda (e2: C).(csubc g e1 e2))
+(ex2 C (\lambda (e2: C).(drop (S n) O (CHead x k t) e2)) (\lambda (e2:
+C).(csubc g e1 e2))) (\lambda (x0: C).(\lambda (H8: (drop (r k n) O x
+x0)).(\lambda (H9: (csubc g e1 x0)).(ex_intro2 C (\lambda (e2: C).(drop (S n)
+O (CHead x k t) e2)) (\lambda (e2: C).(csubc g e1 e2)) x0 (drop_drop k n x x0
+H8 t) H9)))) H7))) c2 H5)))) H4)) (\lambda (H4: (ex5_3 C T A (\lambda (_:
+C).(\lambda (_: T).(\lambda (_: A).(eq K k (Bind Abst))))) (\lambda (c3:
+C).(\lambda (w: T).(\lambda (_: A).(eq C c2 (CHead c3 (Bind Abbr) w)))))
+(\lambda (c3: C).(\lambda (_: T).(\lambda (_: A).(csubc g c c3)))) (\lambda
+(_: C).(\lambda (_: T).(\lambda (a: A).(sc3 g (asucc g a) c t)))) (\lambda
+(c3: C).(\lambda (w: T).(\lambda (a: A).(sc3 g a c3 w)))))).(ex5_3_ind C T A
+(\lambda (_: C).(\lambda (_: T).(\lambda (_: A).(eq K k (Bind Abst)))))
+(\lambda (c3: C).(\lambda (w: T).(\lambda (_: A).(eq C c2 (CHead c3 (Bind
+Abbr) w))))) (\lambda (c3: C).(\lambda (_: T).(\lambda (_: A).(csubc g c
+c3)))) (\lambda (_: C).(\lambda (_: T).(\lambda (a: A).(sc3 g (asucc g a) c
+t)))) (\lambda (c3: C).(\lambda (w: T).(\lambda (a: A).(sc3 g a c3 w)))) (ex2
+C (\lambda (e2: C).(drop (S n) O c2 e2)) (\lambda (e2: C).(csubc g e1 e2)))
+(\lambda (x0: C).(\lambda (x1: T).(\lambda (x2: A).(\lambda (H5: (eq K k
+(Bind Abst))).(\lambda (H6: (eq C c2 (CHead x0 (Bind Abbr) x1))).(\lambda
+(H7: (csubc g c x0)).(\lambda (_: (sc3 g (asucc g x2) c t)).(\lambda (_: (sc3
+g x2 x0 x1)).(eq_ind_r C (CHead x0 (Bind Abbr) x1) (\lambda (c0: C).(ex2 C
+(\lambda (e2: C).(drop (S n) O c0 e2)) (\lambda (e2: C).(csubc g e1 e2))))
+(let H10 \def (eq_ind K k (\lambda (k0: K).(drop (r k0 n) O c e1))
+(drop_gen_drop k c e1 t n H1) (Bind Abst) H5) in (let H11 \def (eq_ind K k
+(\lambda (k0: K).((drop n O (CHead c k0 t) e1) \to (\forall (c3: C).((csubc g
+(CHead c k0 t) c3) \to (ex2 C (\lambda (e2: C).(drop n O c3 e2)) (\lambda
+(e2: C).(csubc g e1 e2))))))) H0 (Bind Abst) H5) in (let H_x0 \def (H e1 (r
+(Bind Abst) n) H10 x0 H7) in (let H12 \def H_x0 in (ex2_ind C (\lambda (e2:
+C).(drop n O x0 e2)) (\lambda (e2: C).(csubc g e1 e2)) (ex2 C (\lambda (e2:
+C).(drop (S n) O (CHead x0 (Bind Abbr) x1) e2)) (\lambda (e2: C).(csubc g e1
+e2))) (\lambda (x: C).(\lambda (H13: (drop n O x0 x)).(\lambda (H14: (csubc g
+e1 x)).(ex_intro2 C (\lambda (e2: C).(drop (S n) O (CHead x0 (Bind Abbr) x1)
+e2)) (\lambda (e2: C).(csubc g e1 e2)) x (drop_drop (Bind Abbr) n x0 x H13
+x1) H14)))) H12))))) c2 H6))))))))) H4)) (\lambda (H4: (ex4_3 B C T (\lambda
+(b: B).(\lambda (c3: C).(\lambda (v2: T).(eq C c2 (CHead c3 (Bind b) v2)))))
+(\lambda (_: B).(\lambda (_: C).(\lambda (_: T).(eq K k (Bind Void)))))
+(\lambda (b: B).(\lambda (_: C).(\lambda (_: T).(not (eq B b Void)))))
+(\lambda (_: B).(\lambda (c3: C).(\lambda (_: T).(csubc g c
+c3)))))).(ex4_3_ind B C T (\lambda (b: B).(\lambda (c3: C).(\lambda (v2:
+T).(eq C c2 (CHead c3 (Bind b) v2))))) (\lambda (_: B).(\lambda (_:
+C).(\lambda (_: T).(eq K k (Bind Void))))) (\lambda (b: B).(\lambda (_:
+C).(\lambda (_: T).(not (eq B b Void))))) (\lambda (_: B).(\lambda (c3:
+C).(\lambda (_: T).(csubc g c c3)))) (ex2 C (\lambda (e2: C).(drop (S n) O c2
+e2)) (\lambda (e2: C).(csubc g e1 e2))) (\lambda (x0: B).(\lambda (x1:
+C).(\lambda (x2: T).(\lambda (H5: (eq C c2 (CHead x1 (Bind x0) x2))).(\lambda
+(H6: (eq K k (Bind Void))).(\lambda (_: (not (eq B x0 Void))).(\lambda (H8:
+(csubc g c x1)).(eq_ind_r C (CHead x1 (Bind x0) x2) (\lambda (c0: C).(ex2 C
+(\lambda (e2: C).(drop (S n) O c0 e2)) (\lambda (e2: C).(csubc g e1 e2))))
+(let H9 \def (eq_ind K k (\lambda (k0: K).(drop (r k0 n) O c e1))
+(drop_gen_drop k c e1 t n H1) (Bind Void) H6) in (let H10 \def (eq_ind K k
+(\lambda (k0: K).((drop n O (CHead c k0 t) e1) \to (\forall (c3: C).((csubc g
+(CHead c k0 t) c3) \to (ex2 C (\lambda (e2: C).(drop n O c3 e2)) (\lambda
+(e2: C).(csubc g e1 e2))))))) H0 (Bind Void) H6) in (let H_x0 \def (H e1 (r
+(Bind Void) n) H9 x1 H8) in (let H11 \def H_x0 in (ex2_ind C (\lambda (e2:
+C).(drop n O x1 e2)) (\lambda (e2: C).(csubc g e1 e2)) (ex2 C (\lambda (e2:
+C).(drop (S n) O (CHead x1 (Bind x0) x2) e2)) (\lambda (e2: C).(csubc g e1
+e2))) (\lambda (x: C).(\lambda (H12: (drop n O x1 x)).(\lambda (H13: (csubc g
+e1 x)).(ex_intro2 C (\lambda (e2: C).(drop (S n) O (CHead x1 (Bind x0) x2)
+e2)) (\lambda (e2: C).(csubc g e1 e2)) x (drop_drop (Bind x0) n x1 x H12 x2)
+H13)))) H11))))) c2 H5)))))))) H4)) H3)))))))) h))))))) c1)).
theorem drop_csubc_trans:
\forall (g: G).(\forall (c2: C).(\forall (e2: C).(\forall (d: nat).(\forall
C).(csubc g (CHead c k t0) c1)))))))) H7 (lift h (r k n) x1) H4) in (eq_ind_r
T (lift h (r k n) x1) (\lambda (t0: T).(ex2 C (\lambda (c1: C).(drop h (S n)
c1 e1)) (\lambda (c1: C).(csubc g (CHead c k t0) c1)))) (let H_x \def
-(csubc_gen_head_l g x0 e1 x1 k H6) in (let H9 \def H_x in (or_ind (ex2 C
+(csubc_gen_head_l g x0 e1 x1 k H6) in (let H9 \def H_x in (or3_ind (ex2 C
(\lambda (c3: C).(eq C e1 (CHead c3 k x1))) (\lambda (c3: C).(csubc g x0
c3))) (ex5_3 C T A (\lambda (_: C).(\lambda (_: T).(\lambda (_: A).(eq K k
(Bind Abst))))) (\lambda (c3: C).(\lambda (w: T).(\lambda (_: A).(eq C e1
(CHead c3 (Bind Abbr) w))))) (\lambda (c3: C).(\lambda (_: T).(\lambda (_:
A).(csubc g x0 c3)))) (\lambda (_: C).(\lambda (_: T).(\lambda (a: A).(sc3 g
(asucc g a) x0 x1)))) (\lambda (c3: C).(\lambda (w: T).(\lambda (a: A).(sc3 g
-a c3 w))))) (ex2 C (\lambda (c1: C).(drop h (S n) c1 e1)) (\lambda (c1:
-C).(csubc g (CHead c k (lift h (r k n) x1)) c1))) (\lambda (H10: (ex2 C
-(\lambda (c3: C).(eq C e1 (CHead c3 k x1))) (\lambda (c3: C).(csubc g x0
-c3)))).(ex2_ind C (\lambda (c3: C).(eq C e1 (CHead c3 k x1))) (\lambda (c3:
-C).(csubc g x0 c3)) (ex2 C (\lambda (c1: C).(drop h (S n) c1 e1)) (\lambda
-(c1: C).(csubc g (CHead c k (lift h (r k n) x1)) c1))) (\lambda (x:
-C).(\lambda (H11: (eq C e1 (CHead x k x1))).(\lambda (H12: (csubc g x0
-x)).(eq_ind_r C (CHead x k x1) (\lambda (c0: C).(ex2 C (\lambda (c1: C).(drop
-h (S n) c1 c0)) (\lambda (c1: C).(csubc g (CHead c k (lift h (r k n) x1))
-c1)))) (let H_x0 \def (H x0 (r k n) h H5 x H12) in (let H13 \def H_x0 in
-(ex2_ind C (\lambda (c1: C).(drop h (r k n) c1 x)) (\lambda (c1: C).(csubc g
-c c1)) (ex2 C (\lambda (c1: C).(drop h (S n) c1 (CHead x k x1))) (\lambda
-(c1: C).(csubc g (CHead c k (lift h (r k n) x1)) c1))) (\lambda (x2:
+a c3 w))))) (ex4_3 B C T (\lambda (b: B).(\lambda (c3: C).(\lambda (v2:
+T).(eq C e1 (CHead c3 (Bind b) v2))))) (\lambda (_: B).(\lambda (_:
+C).(\lambda (_: T).(eq K k (Bind Void))))) (\lambda (b: B).(\lambda (_:
+C).(\lambda (_: T).(not (eq B b Void))))) (\lambda (_: B).(\lambda (c3:
+C).(\lambda (_: T).(csubc g x0 c3))))) (ex2 C (\lambda (c1: C).(drop h (S n)
+c1 e1)) (\lambda (c1: C).(csubc g (CHead c k (lift h (r k n) x1)) c1)))
+(\lambda (H10: (ex2 C (\lambda (c3: C).(eq C e1 (CHead c3 k x1))) (\lambda
+(c3: C).(csubc g x0 c3)))).(ex2_ind C (\lambda (c3: C).(eq C e1 (CHead c3 k
+x1))) (\lambda (c3: C).(csubc g x0 c3)) (ex2 C (\lambda (c1: C).(drop h (S n)
+c1 e1)) (\lambda (c1: C).(csubc g (CHead c k (lift h (r k n) x1)) c1)))
+(\lambda (x: C).(\lambda (H11: (eq C e1 (CHead x k x1))).(\lambda (H12:
+(csubc g x0 x)).(eq_ind_r C (CHead x k x1) (\lambda (c0: C).(ex2 C (\lambda
+(c1: C).(drop h (S n) c1 c0)) (\lambda (c1: C).(csubc g (CHead c k (lift h (r
+k n) x1)) c1)))) (let H_x0 \def (H x0 (r k n) h H5 x H12) in (let H13 \def
+H_x0 in (ex2_ind C (\lambda (c1: C).(drop h (r k n) c1 x)) (\lambda (c1:
+C).(csubc g c c1)) (ex2 C (\lambda (c1: C).(drop h (S n) c1 (CHead x k x1)))
+(\lambda (c1: C).(csubc g (CHead c k (lift h (r k n) x1)) c1))) (\lambda (x2:
C).(\lambda (H14: (drop h (r k n) x2 x)).(\lambda (H15: (csubc g c
x2)).(ex_intro2 C (\lambda (c1: C).(drop h (S n) c1 (CHead x k x1))) (\lambda
(c1: C).(csubc g (CHead c k (lift h (r k n) x1)) c1)) (CHead x2 k (lift h (r
n) x1)) c1)) (CHead x (Bind Abbr) (lift h n x3)) (drop_skip_bind h n x x2 H19
Abbr x3) (csubc_abst g c x H20 (lift h (r (Bind Abst) n) x1) x4 (sc3_lift g
(asucc g x4) x0 x1 H14 c h (r (Bind Abst) n) H17) (lift h n x3) (sc3_lift g
-x4 x2 x3 H15 x h n H19)))))) H18))) k H11))) e1 H12))))))))) H10)) H9))) t
-H4))))))))) (drop_gen_skip_l c e2 t h n k H1)))))))) d))))))) c2)).
+x4 x2 x3 H15 x h n H19)))))) H18))) k H11))) e1 H12))))))))) H10)) (\lambda
+(H10: (ex4_3 B C T (\lambda (b: B).(\lambda (c3: C).(\lambda (v2: T).(eq C e1
+(CHead c3 (Bind b) v2))))) (\lambda (_: B).(\lambda (_: C).(\lambda (_:
+T).(eq K k (Bind Void))))) (\lambda (b: B).(\lambda (_: C).(\lambda (_:
+T).(not (eq B b Void))))) (\lambda (_: B).(\lambda (c3: C).(\lambda (_:
+T).(csubc g x0 c3)))))).(ex4_3_ind B C T (\lambda (b: B).(\lambda (c3:
+C).(\lambda (v2: T).(eq C e1 (CHead c3 (Bind b) v2))))) (\lambda (_:
+B).(\lambda (_: C).(\lambda (_: T).(eq K k (Bind Void))))) (\lambda (b:
+B).(\lambda (_: C).(\lambda (_: T).(not (eq B b Void))))) (\lambda (_:
+B).(\lambda (c3: C).(\lambda (_: T).(csubc g x0 c3)))) (ex2 C (\lambda (c1:
+C).(drop h (S n) c1 e1)) (\lambda (c1: C).(csubc g (CHead c k (lift h (r k n)
+x1)) c1))) (\lambda (x2: B).(\lambda (x3: C).(\lambda (x4: T).(\lambda (H11:
+(eq C e1 (CHead x3 (Bind x2) x4))).(\lambda (H12: (eq K k (Bind
+Void))).(\lambda (H13: (not (eq B x2 Void))).(\lambda (H14: (csubc g x0
+x3)).(eq_ind_r C (CHead x3 (Bind x2) x4) (\lambda (c0: C).(ex2 C (\lambda
+(c1: C).(drop h (S n) c1 c0)) (\lambda (c1: C).(csubc g (CHead c k (lift h (r
+k n) x1)) c1)))) (let H15 \def (eq_ind K k (\lambda (k0: K).(\forall (h0:
+nat).((drop h0 n (CHead c k0 (lift h (r k0 n) x1)) (CHead x0 k0 x1)) \to
+(\forall (e3: C).((csubc g (CHead x0 k0 x1) e3) \to (ex2 C (\lambda (c1:
+C).(drop h0 n c1 e3)) (\lambda (c1: C).(csubc g (CHead c k0 (lift h (r k0 n)
+x1)) c1)))))))) H8 (Bind Void) H12) in (let H16 \def (eq_ind K k (\lambda
+(k0: K).(drop h (r k0 n) c x0)) H5 (Bind Void) H12) in (eq_ind_r K (Bind
+Void) (\lambda (k0: K).(ex2 C (\lambda (c1: C).(drop h (S n) c1 (CHead x3
+(Bind x2) x4))) (\lambda (c1: C).(csubc g (CHead c k0 (lift h (r k0 n) x1))
+c1)))) (let H_x0 \def (H x0 (r (Bind Void) n) h H16 x3 H14) in (let H17 \def
+H_x0 in (ex2_ind C (\lambda (c1: C).(drop h n c1 x3)) (\lambda (c1: C).(csubc
+g c c1)) (ex2 C (\lambda (c1: C).(drop h (S n) c1 (CHead x3 (Bind x2) x4)))
+(\lambda (c1: C).(csubc g (CHead c (Bind Void) (lift h (r (Bind Void) n) x1))
+c1))) (\lambda (x: C).(\lambda (H18: (drop h n x x3)).(\lambda (H19: (csubc g
+c x)).(ex_intro2 C (\lambda (c1: C).(drop h (S n) c1 (CHead x3 (Bind x2)
+x4))) (\lambda (c1: C).(csubc g (CHead c (Bind Void) (lift h (r (Bind Void)
+n) x1)) c1)) (CHead x (Bind x2) (lift h n x4)) (drop_skip_bind h n x x3 H18
+x2 x4) (csubc_void g c x H19 x2 H13 (lift h (r (Bind Void) n) x1) (lift h n
+x4)))))) H17))) k H12))) e1 H11)))))))) H10)) H9))) t H4)))))))))
+(drop_gen_skip_l c e2 t h n k H1)))))))) d))))))) c2)).
theorem csubc_drop_conf_rev:
\forall (g: G).(\forall (c2: C).(\forall (e2: C).(\forall (d: nat).(\forall
g c1 (CHead c k t0))))))))) H7 (lift h (r k n) x1) H4) in (eq_ind_r T (lift h
(r k n) x1) (\lambda (t0: T).(ex2 C (\lambda (c1: C).(drop h (S n) c1 e1))
(\lambda (c1: C).(csubc g c1 (CHead c k t0))))) (let H_x \def
-(csubc_gen_head_r g x0 e1 x1 k H6) in (let H9 \def H_x in (or_ind (ex2 C
+(csubc_gen_head_r g x0 e1 x1 k H6) in (let H9 \def H_x in (or3_ind (ex2 C
(\lambda (c1: C).(eq C e1 (CHead c1 k x1))) (\lambda (c1: C).(csubc g c1
x0))) (ex5_3 C T A (\lambda (_: C).(\lambda (_: T).(\lambda (_: A).(eq K k
(Bind Abbr))))) (\lambda (c1: C).(\lambda (v: T).(\lambda (_: A).(eq C e1
(CHead c1 (Bind Abst) v))))) (\lambda (c1: C).(\lambda (_: T).(\lambda (_:
A).(csubc g c1 x0)))) (\lambda (c1: C).(\lambda (v: T).(\lambda (a: A).(sc3 g
(asucc g a) c1 v)))) (\lambda (_: C).(\lambda (_: T).(\lambda (a: A).(sc3 g a
-x0 x1))))) (ex2 C (\lambda (c1: C).(drop h (S n) c1 e1)) (\lambda (c1:
-C).(csubc g c1 (CHead c k (lift h (r k n) x1))))) (\lambda (H10: (ex2 C
+x0 x1))))) (ex4_3 B C T (\lambda (_: B).(\lambda (c1: C).(\lambda (v1: T).(eq
+C e1 (CHead c1 (Bind Void) v1))))) (\lambda (b: B).(\lambda (_: C).(\lambda
+(_: T).(eq K k (Bind b))))) (\lambda (b: B).(\lambda (_: C).(\lambda (_:
+T).(not (eq B b Void))))) (\lambda (_: B).(\lambda (c1: C).(\lambda (_:
+T).(csubc g c1 x0))))) (ex2 C (\lambda (c1: C).(drop h (S n) c1 e1)) (\lambda
+(c1: C).(csubc g c1 (CHead c k (lift h (r k n) x1))))) (\lambda (H10: (ex2 C
(\lambda (c1: C).(eq C e1 (CHead c1 k x1))) (\lambda (c1: C).(csubc g c1
x0)))).(ex2_ind C (\lambda (c1: C).(eq C e1 (CHead c1 k x1))) (\lambda (c1:
C).(csubc g c1 x0)) (ex2 C (\lambda (c1: C).(drop h (S n) c1 e1)) (\lambda
(Bind Abst) (lift h n x3)) (drop_skip_bind h n x x2 H19 Abst x3) (csubc_abst
g x c H20 (lift h n x3) x4 (sc3_lift g (asucc g x4) x2 x3 H14 x h n H19)
(lift h (r (Bind Abbr) n) x1) (sc3_lift g x4 x0 x1 H15 c h (r (Bind Abbr) n)
-H17)))))) H18))) k H11))) e1 H12))))))))) H10)) H9))) t H4)))))))))
-(drop_gen_skip_l c e2 t h n k H1)))))))) d))))))) c2)).
+H17)))))) H18))) k H11))) e1 H12))))))))) H10)) (\lambda (H10: (ex4_3 B C T
+(\lambda (_: B).(\lambda (c1: C).(\lambda (v1: T).(eq C e1 (CHead c1 (Bind
+Void) v1))))) (\lambda (b: B).(\lambda (_: C).(\lambda (_: T).(eq K k (Bind
+b))))) (\lambda (b: B).(\lambda (_: C).(\lambda (_: T).(not (eq B b Void)))))
+(\lambda (_: B).(\lambda (c1: C).(\lambda (_: T).(csubc g c1
+x0)))))).(ex4_3_ind B C T (\lambda (_: B).(\lambda (c1: C).(\lambda (v1:
+T).(eq C e1 (CHead c1 (Bind Void) v1))))) (\lambda (b: B).(\lambda (_:
+C).(\lambda (_: T).(eq K k (Bind b))))) (\lambda (b: B).(\lambda (_:
+C).(\lambda (_: T).(not (eq B b Void))))) (\lambda (_: B).(\lambda (c1:
+C).(\lambda (_: T).(csubc g c1 x0)))) (ex2 C (\lambda (c1: C).(drop h (S n)
+c1 e1)) (\lambda (c1: C).(csubc g c1 (CHead c k (lift h (r k n) x1)))))
+(\lambda (x2: B).(\lambda (x3: C).(\lambda (x4: T).(\lambda (H11: (eq C e1
+(CHead x3 (Bind Void) x4))).(\lambda (H12: (eq K k (Bind x2))).(\lambda (H13:
+(not (eq B x2 Void))).(\lambda (H14: (csubc g x3 x0)).(eq_ind_r C (CHead x3
+(Bind Void) x4) (\lambda (c0: C).(ex2 C (\lambda (c1: C).(drop h (S n) c1
+c0)) (\lambda (c1: C).(csubc g c1 (CHead c k (lift h (r k n) x1)))))) (let
+H15 \def (eq_ind K k (\lambda (k0: K).(\forall (h0: nat).((drop h0 n (CHead c
+k0 (lift h (r k0 n) x1)) (CHead x0 k0 x1)) \to (\forall (e3: C).((csubc g e3
+(CHead x0 k0 x1)) \to (ex2 C (\lambda (c1: C).(drop h0 n c1 e3)) (\lambda
+(c1: C).(csubc g c1 (CHead c k0 (lift h (r k0 n) x1)))))))))) H8 (Bind x2)
+H12) in (let H16 \def (eq_ind K k (\lambda (k0: K).(drop h (r k0 n) c x0)) H5
+(Bind x2) H12) in (eq_ind_r K (Bind x2) (\lambda (k0: K).(ex2 C (\lambda (c1:
+C).(drop h (S n) c1 (CHead x3 (Bind Void) x4))) (\lambda (c1: C).(csubc g c1
+(CHead c k0 (lift h (r k0 n) x1)))))) (let H_x0 \def (H x0 (r (Bind x2) n) h
+H16 x3 H14) in (let H17 \def H_x0 in (ex2_ind C (\lambda (c1: C).(drop h n c1
+x3)) (\lambda (c1: C).(csubc g c1 c)) (ex2 C (\lambda (c1: C).(drop h (S n)
+c1 (CHead x3 (Bind Void) x4))) (\lambda (c1: C).(csubc g c1 (CHead c (Bind
+x2) (lift h (r (Bind x2) n) x1))))) (\lambda (x: C).(\lambda (H18: (drop h n
+x x3)).(\lambda (H19: (csubc g x c)).(ex_intro2 C (\lambda (c1: C).(drop h (S
+n) c1 (CHead x3 (Bind Void) x4))) (\lambda (c1: C).(csubc g c1 (CHead c (Bind
+x2) (lift h (r (Bind x2) n) x1)))) (CHead x (Bind Void) (lift h n x4))
+(drop_skip_bind h n x x3 H18 Void x4) (csubc_void g x c H19 x2 H13 (lift h n
+x4) (lift h (r (Bind x2) n) x1)))))) H17))) k H12))) e1 H11)))))))) H10))
+H9))) t H4))))))))) (drop_gen_skip_l c e2 t h n k H1)))))))) d))))))) c2)).
projects / helm.git / blobdiff