--- /dev/null
+(**************************************************************************)
+(* ___ *)
+(* ||M|| *)
+(* ||A|| A project by Andrea Asperti *)
+(* ||T|| *)
+(* ||I|| Developers: *)
+(* ||T|| The HELM team. *)
+(* ||A|| http://helm.cs.unibo.it *)
+(* \ / *)
+(* \ / This file is distributed under the terms of the *)
+(* v GNU General Public License Version 2 *)
+(* *)
+(**************************************************************************)
+
+(* This file was automatically generated: do not edit *********************)
+
+include "basic_1A/csubc/fwd.ma".
+
+include "basic_1A/clear/fwd.ma".
+
+lemma csubc_clear_conf:
+ \forall (g: G).(\forall (c1: C).(\forall (e1: C).((clear c1 e1) \to (\forall
+(c2: C).((csubc g c1 c2) \to (ex2 C (\lambda (e2: C).(clear c2 e2)) (\lambda
+(e2: C).(csubc g e1 e2))))))))
+\def
+ \lambda (g: G).(\lambda (c1: C).(\lambda (e1: C).(\lambda (H: (clear c1
+e1)).(clear_ind (\lambda (c: C).(\lambda (c0: C).(\forall (c2: C).((csubc g c
+c2) \to (ex2 C (\lambda (e2: C).(clear c2 e2)) (\lambda (e2: C).(csubc g c0
+e2))))))) (\lambda (b: B).(\lambda (e: C).(\lambda (u: T).(\lambda (c2:
+C).(\lambda (H0: (csubc g (CHead e (Bind b) u) c2)).(let H_x \def
+(csubc_gen_head_l g e c2 u (Bind b) H0) in (let H1 \def H_x in (or3_ind (ex2
+C (\lambda (c3: C).(eq C c2 (CHead c3 (Bind b) u))) (\lambda (c3: C).(csubc g
+e c3))) (ex5_3 C T A (\lambda (_: C).(\lambda (_: T).(\lambda (_: A).(eq K
+(Bind b) (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 e c3)))) (\lambda (_: C).(\lambda (_: T).(\lambda (a: A).(sc3
+g (asucc g a) e u)))) (\lambda (c3: C).(\lambda (w: T).(\lambda (a: A).(sc3 g
+a c3 w))))) (ex4_3 B C T (\lambda (b0: B).(\lambda (c3: C).(\lambda (v2:
+T).(eq C c2 (CHead c3 (Bind b0) v2))))) (\lambda (_: B).(\lambda (_:
+C).(\lambda (_: T).(eq K (Bind b) (Bind Void))))) (\lambda (b0: B).(\lambda
+(_: C).(\lambda (_: T).(not (eq B b0 Void))))) (\lambda (_: B).(\lambda (c3:
+C).(\lambda (_: T).(csubc g e c3))))) (ex2 C (\lambda (e2: C).(clear c2 e2))
+(\lambda (e2: C).(csubc g (CHead e (Bind b) u) e2))) (\lambda (H2: (ex2 C
+(\lambda (c3: C).(eq C c2 (CHead c3 (Bind b) u))) (\lambda (c3: C).(csubc g e
+c3)))).(ex2_ind C (\lambda (c3: C).(eq C c2 (CHead c3 (Bind b) u))) (\lambda
+(c3: C).(csubc g e c3)) (ex2 C (\lambda (e2: C).(clear c2 e2)) (\lambda (e2:
+C).(csubc g (CHead e (Bind b) u) e2))) (\lambda (x: C).(\lambda (H3: (eq C c2
+(CHead x (Bind b) u))).(\lambda (H4: (csubc g e x)).(eq_ind_r C (CHead x
+(Bind b) u) (\lambda (c: C).(ex2 C (\lambda (e2: C).(clear c e2)) (\lambda
+(e2: C).(csubc g (CHead e (Bind b) u) e2)))) (ex_intro2 C (\lambda (e2:
+C).(clear (CHead x (Bind b) u) e2)) (\lambda (e2: C).(csubc g (CHead e (Bind
+b) u) e2)) (CHead x (Bind b) u) (clear_bind b x u) (csubc_head g e x H4 (Bind
+b) u)) c2 H3)))) H2)) (\lambda (H2: (ex5_3 C T A (\lambda (_: C).(\lambda (_:
+T).(\lambda (_: A).(eq K (Bind b) (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 e c3)))) (\lambda (_: C).(\lambda
+(_: T).(\lambda (a: A).(sc3 g (asucc g a) e u)))) (\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 (Bind b) (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 e c3)))) (\lambda
+(_: C).(\lambda (_: T).(\lambda (a: A).(sc3 g (asucc g a) e u)))) (\lambda
+(c3: C).(\lambda (w: T).(\lambda (a: A).(sc3 g a c3 w)))) (ex2 C (\lambda
+(e2: C).(clear c2 e2)) (\lambda (e2: C).(csubc g (CHead e (Bind b) u) e2)))
+(\lambda (x0: C).(\lambda (x1: T).(\lambda (x2: A).(\lambda (H3: (eq K (Bind
+b) (Bind Abst))).(\lambda (H4: (eq C c2 (CHead x0 (Bind Abbr) x1))).(\lambda
+(H5: (csubc g e x0)).(\lambda (H6: (sc3 g (asucc g x2) e u)).(\lambda (H7:
+(sc3 g x2 x0 x1)).(eq_ind_r C (CHead x0 (Bind Abbr) x1) (\lambda (c: C).(ex2
+C (\lambda (e2: C).(clear c e2)) (\lambda (e2: C).(csubc g (CHead e (Bind b)
+u) e2)))) (let H8 \def (f_equal K B (\lambda (e0: K).(match e0 with [(Bind
+b0) \Rightarrow b0 | (Flat _) \Rightarrow b])) (Bind b) (Bind Abst) H3) in
+(eq_ind_r B Abst (\lambda (b0: B).(ex2 C (\lambda (e2: C).(clear (CHead x0
+(Bind Abbr) x1) e2)) (\lambda (e2: C).(csubc g (CHead e (Bind b0) u) e2))))
+(ex_intro2 C (\lambda (e2: C).(clear (CHead x0 (Bind Abbr) x1) e2)) (\lambda
+(e2: C).(csubc g (CHead e (Bind Abst) u) e2)) (CHead x0 (Bind Abbr) x1)
+(clear_bind Abbr x0 x1) (csubc_abst g e x0 H5 u x2 H6 x1 H7)) b H8)) c2
+H4))))))))) H2)) (\lambda (H2: (ex4_3 B C T (\lambda (b0: B).(\lambda (c3:
+C).(\lambda (v2: T).(eq C c2 (CHead c3 (Bind b0) v2))))) (\lambda (_:
+B).(\lambda (_: C).(\lambda (_: T).(eq K (Bind b) (Bind Void))))) (\lambda
+(b0: B).(\lambda (_: C).(\lambda (_: T).(not (eq B b0 Void))))) (\lambda (_:
+B).(\lambda (c3: C).(\lambda (_: T).(csubc g e c3)))))).(ex4_3_ind B C T
+(\lambda (b0: B).(\lambda (c3: C).(\lambda (v2: T).(eq C c2 (CHead c3 (Bind
+b0) v2))))) (\lambda (_: B).(\lambda (_: C).(\lambda (_: T).(eq K (Bind b)
+(Bind Void))))) (\lambda (b0: B).(\lambda (_: C).(\lambda (_: T).(not (eq B
+b0 Void))))) (\lambda (_: B).(\lambda (c3: C).(\lambda (_: T).(csubc g e
+c3)))) (ex2 C (\lambda (e2: C).(clear c2 e2)) (\lambda (e2: C).(csubc g
+(CHead e (Bind b) u) e2))) (\lambda (x0: B).(\lambda (x1: C).(\lambda (x2:
+T).(\lambda (H3: (eq C c2 (CHead x1 (Bind x0) x2))).(\lambda (H4: (eq K (Bind
+b) (Bind Void))).(\lambda (H5: (not (eq B x0 Void))).(\lambda (H6: (csubc g e
+x1)).(eq_ind_r C (CHead x1 (Bind x0) x2) (\lambda (c: C).(ex2 C (\lambda (e2:
+C).(clear c e2)) (\lambda (e2: C).(csubc g (CHead e (Bind b) u) e2)))) (let
+H7 \def (f_equal K B (\lambda (e0: K).(match e0 with [(Bind b0) \Rightarrow
+b0 | (Flat _) \Rightarrow b])) (Bind b) (Bind Void) H4) in (eq_ind_r B Void
+(\lambda (b0: B).(ex2 C (\lambda (e2: C).(clear (CHead x1 (Bind x0) x2) e2))
+(\lambda (e2: C).(csubc g (CHead e (Bind b0) u) e2)))) (ex_intro2 C (\lambda
+(e2: C).(clear (CHead x1 (Bind x0) x2) e2)) (\lambda (e2: C).(csubc g (CHead
+e (Bind Void) u) e2)) (CHead x1 (Bind x0) x2) (clear_bind x0 x1 x2)
+(csubc_void g e x1 H6 x0 H5 u x2)) b H7)) c2 H3)))))))) H2)) H1))))))))
+(\lambda (e: C).(\lambda (c: C).(\lambda (_: (clear e c)).(\lambda (H1:
+((\forall (c2: C).((csubc g e c2) \to (ex2 C (\lambda (e2: C).(clear c2 e2))
+(\lambda (e2: C).(csubc g c e2))))))).(\lambda (f: F).(\lambda (u:
+T).(\lambda (c2: C).(\lambda (H2: (csubc g (CHead e (Flat f) u) c2)).(let H_x
+\def (csubc_gen_head_l g e c2 u (Flat f) H2) in (let H3 \def H_x in (or3_ind
+(ex2 C (\lambda (c3: C).(eq C c2 (CHead c3 (Flat f) u))) (\lambda (c3:
+C).(csubc g e c3))) (ex5_3 C T A (\lambda (_: C).(\lambda (_: T).(\lambda (_:
+A).(eq K (Flat f) (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 e c3)))) (\lambda (_: C).(\lambda (_: T).(\lambda
+(a: A).(sc3 g (asucc g a) e u)))) (\lambda (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 (Flat f) (Bind Void))))) (\lambda
+(b: B).(\lambda (_: C).(\lambda (_: T).(not (eq B b Void))))) (\lambda (_:
+B).(\lambda (c3: C).(\lambda (_: T).(csubc g e c3))))) (ex2 C (\lambda (e2:
+C).(clear c2 e2)) (\lambda (e2: C).(csubc g c e2))) (\lambda (H4: (ex2 C
+(\lambda (c3: C).(eq C c2 (CHead c3 (Flat f) u))) (\lambda (c3: C).(csubc g e
+c3)))).(ex2_ind C (\lambda (c3: C).(eq C c2 (CHead c3 (Flat f) u))) (\lambda
+(c3: C).(csubc g e c3)) (ex2 C (\lambda (e2: C).(clear c2 e2)) (\lambda (e2:
+C).(csubc g c e2))) (\lambda (x: C).(\lambda (H5: (eq C c2 (CHead x (Flat f)
+u))).(\lambda (H6: (csubc g e x)).(eq_ind_r C (CHead x (Flat f) u) (\lambda
+(c0: C).(ex2 C (\lambda (e2: C).(clear c0 e2)) (\lambda (e2: C).(csubc g c
+e2)))) (let H_x0 \def (H1 x H6) in (let H7 \def H_x0 in (ex2_ind C (\lambda
+(e2: C).(clear x e2)) (\lambda (e2: C).(csubc g c e2)) (ex2 C (\lambda (e2:
+C).(clear (CHead x (Flat f) u) e2)) (\lambda (e2: C).(csubc g c e2)))
+(\lambda (x0: C).(\lambda (H8: (clear x x0)).(\lambda (H9: (csubc g c
+x0)).(ex_intro2 C (\lambda (e2: C).(clear (CHead x (Flat f) u) e2)) (\lambda
+(e2: C).(csubc g c e2)) x0 (clear_flat x x0 H8 f u) H9)))) H7))) c2 H5))))
+H4)) (\lambda (H4: (ex5_3 C T A (\lambda (_: C).(\lambda (_: T).(\lambda (_:
+A).(eq K (Flat f) (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 e c3)))) (\lambda (_: C).(\lambda (_: T).(\lambda
+(a: A).(sc3 g (asucc g a) e u)))) (\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 (Flat f) (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 e c3)))) (\lambda (_: C).(\lambda
+(_: T).(\lambda (a: A).(sc3 g (asucc g a) e u)))) (\lambda (c3: C).(\lambda
+(w: T).(\lambda (a: A).(sc3 g a c3 w)))) (ex2 C (\lambda (e2: C).(clear c2
+e2)) (\lambda (e2: C).(csubc g c e2))) (\lambda (x0: C).(\lambda (x1:
+T).(\lambda (x2: A).(\lambda (H5: (eq K (Flat f) (Bind Abst))).(\lambda (H6:
+(eq C c2 (CHead x0 (Bind Abbr) x1))).(\lambda (_: (csubc g e x0)).(\lambda
+(_: (sc3 g (asucc g x2) e u)).(\lambda (_: (sc3 g x2 x0 x1)).(eq_ind_r C
+(CHead x0 (Bind Abbr) x1) (\lambda (c0: C).(ex2 C (\lambda (e2: C).(clear c0
+e2)) (\lambda (e2: C).(csubc g c e2)))) (let H10 \def (eq_ind K (Flat f)
+(\lambda (ee: K).(match ee with [(Bind _) \Rightarrow False | (Flat _)
+\Rightarrow True])) I (Bind Abst) H5) in (False_ind (ex2 C (\lambda (e2:
+C).(clear (CHead x0 (Bind Abbr) x1) e2)) (\lambda (e2: C).(csubc g c e2)))
+H10)) 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 (Flat f) (Bind Void))))) (\lambda
+(b: B).(\lambda (_: C).(\lambda (_: T).(not (eq B b Void))))) (\lambda (_:
+B).(\lambda (c3: C).(\lambda (_: T).(csubc g e 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 (Flat f) (Bind
+Void))))) (\lambda (b: B).(\lambda (_: C).(\lambda (_: T).(not (eq B b
+Void))))) (\lambda (_: B).(\lambda (c3: C).(\lambda (_: T).(csubc g e c3))))
+(ex2 C (\lambda (e2: C).(clear c2 e2)) (\lambda (e2: C).(csubc g c e2)))
+(\lambda (x0: B).(\lambda (x1: C).(\lambda (x2: T).(\lambda (H5: (eq C c2
+(CHead x1 (Bind x0) x2))).(\lambda (H6: (eq K (Flat f) (Bind Void))).(\lambda
+(_: (not (eq B x0 Void))).(\lambda (_: (csubc g e x1)).(eq_ind_r C (CHead x1
+(Bind x0) x2) (\lambda (c0: C).(ex2 C (\lambda (e2: C).(clear c0 e2))
+(\lambda (e2: C).(csubc g c e2)))) (let H9 \def (eq_ind K (Flat f) (\lambda
+(ee: K).(match ee with [(Bind _) \Rightarrow False | (Flat _) \Rightarrow
+True])) I (Bind Void) H6) in (False_ind (ex2 C (\lambda (e2: C).(clear (CHead
+x1 (Bind x0) x2) e2)) (\lambda (e2: C).(csubc g c e2))) H9)) c2 H5))))))))
+H4)) H3))))))))))) c1 e1 H)))).
+
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