--- /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 "LambdaDelta-1/getl/defs.ma".
+
+include "LambdaDelta-1/drop/fwd.ma".
+
+include "LambdaDelta-1/clear/fwd.ma".
+
+theorem getl_gen_all:
+ \forall (c1: C).(\forall (c2: C).(\forall (i: nat).((getl i c1 c2) \to (ex2
+C (\lambda (e: C).(drop i O c1 e)) (\lambda (e: C).(clear e c2))))))
+\def
+ \lambda (c1: C).(\lambda (c2: C).(\lambda (i: nat).(\lambda (H: (getl i c1
+c2)).(getl_ind i c1 c2 (ex2 C (\lambda (e: C).(drop i O c1 e)) (\lambda (e:
+C).(clear e c2))) (\lambda (e: C).(\lambda (H0: (drop i O c1 e)).(\lambda
+(H1: (clear e c2)).(ex_intro2 C (\lambda (e0: C).(drop i O c1 e0)) (\lambda
+(e0: C).(clear e0 c2)) e H0 H1)))) H)))).
+
+theorem getl_gen_sort:
+ \forall (n: nat).(\forall (h: nat).(\forall (x: C).((getl h (CSort n) x) \to
+(\forall (P: Prop).P))))
+\def
+ \lambda (n: nat).(\lambda (h: nat).(\lambda (x: C).(\lambda (H: (getl h
+(CSort n) x)).(\lambda (P: Prop).(let H0 \def (getl_gen_all (CSort n) x h H)
+in (ex2_ind C (\lambda (e: C).(drop h O (CSort n) e)) (\lambda (e: C).(clear
+e x)) P (\lambda (x0: C).(\lambda (H1: (drop h O (CSort n) x0)).(\lambda (H2:
+(clear x0 x)).(and3_ind (eq C x0 (CSort n)) (eq nat h O) (eq nat O O) P
+(\lambda (H3: (eq C x0 (CSort n))).(\lambda (_: (eq nat h O)).(\lambda (_:
+(eq nat O O)).(let H6 \def (eq_ind C x0 (\lambda (c: C).(clear c x)) H2
+(CSort n) H3) in (clear_gen_sort x n H6 P))))) (drop_gen_sort n h O x0
+H1))))) H0)))))).
+
+theorem getl_gen_O:
+ \forall (e: C).(\forall (x: C).((getl O e x) \to (clear e x)))
+\def
+ \lambda (e: C).(\lambda (x: C).(\lambda (H: (getl O e x)).(let H0 \def
+(getl_gen_all e x O H) in (ex2_ind C (\lambda (e0: C).(drop O O e e0))
+(\lambda (e0: C).(clear e0 x)) (clear e x) (\lambda (x0: C).(\lambda (H1:
+(drop O O e x0)).(\lambda (H2: (clear x0 x)).(let H3 \def (eq_ind_r C x0
+(\lambda (c: C).(clear c x)) H2 e (drop_gen_refl e x0 H1)) in H3)))) H0)))).
+
+theorem getl_gen_S:
+ \forall (k: K).(\forall (c: C).(\forall (x: C).(\forall (u: T).(\forall (h:
+nat).((getl (S h) (CHead c k u) x) \to (getl (r k h) c x))))))
+\def
+ \lambda (k: K).(\lambda (c: C).(\lambda (x: C).(\lambda (u: T).(\lambda (h:
+nat).(\lambda (H: (getl (S h) (CHead c k u) x)).(let H0 \def (getl_gen_all
+(CHead c k u) x (S h) H) in (ex2_ind C (\lambda (e: C).(drop (S h) O (CHead c
+k u) e)) (\lambda (e: C).(clear e x)) (getl (r k h) c x) (\lambda (x0:
+C).(\lambda (H1: (drop (S h) O (CHead c k u) x0)).(\lambda (H2: (clear x0
+x)).(getl_intro (r k h) c x x0 (drop_gen_drop k c x0 u h H1) H2)))) H0))))))).
+
+theorem getl_gen_flat:
+ \forall (f: F).(\forall (e: C).(\forall (d: C).(\forall (v: T).(\forall (i:
+nat).((getl i (CHead e (Flat f) v) d) \to (getl i e d))))))
+\def
+ \lambda (f: F).(\lambda (e: C).(\lambda (d: C).(\lambda (v: T).(\lambda (i:
+nat).(nat_ind (\lambda (n: nat).((getl n (CHead e (Flat f) v) d) \to (getl n
+e d))) (\lambda (H: (getl O (CHead e (Flat f) v) d)).(getl_intro O e d e
+(drop_refl e) (clear_gen_flat f e d v (getl_gen_O (CHead e (Flat f) v) d
+H)))) (\lambda (n: nat).(\lambda (_: (((getl n (CHead e (Flat f) v) d) \to
+(getl n e d)))).(\lambda (H0: (getl (S n) (CHead e (Flat f) v)
+d)).(getl_gen_S (Flat f) e d v n H0)))) i))))).
+
+theorem getl_gen_bind:
+ \forall (b: B).(\forall (e: C).(\forall (d: C).(\forall (v: T).(\forall (i:
+nat).((getl i (CHead e (Bind b) v) d) \to (or (land (eq nat i O) (eq C d
+(CHead e (Bind b) v))) (ex2 nat (\lambda (j: nat).(eq nat i (S j))) (\lambda
+(j: nat).(getl j e d)))))))))
+\def
+ \lambda (b: B).(\lambda (e: C).(\lambda (d: C).(\lambda (v: T).(\lambda (i:
+nat).(nat_ind (\lambda (n: nat).((getl n (CHead e (Bind b) v) d) \to (or
+(land (eq nat n O) (eq C d (CHead e (Bind b) v))) (ex2 nat (\lambda (j:
+nat).(eq nat n (S j))) (\lambda (j: nat).(getl j e d)))))) (\lambda (H: (getl
+O (CHead e (Bind b) v) d)).(eq_ind_r C (CHead e (Bind b) v) (\lambda (c:
+C).(or (land (eq nat O O) (eq C c (CHead e (Bind b) v))) (ex2 nat (\lambda
+(j: nat).(eq nat O (S j))) (\lambda (j: nat).(getl j e c))))) (or_introl
+(land (eq nat O O) (eq C (CHead e (Bind b) v) (CHead e (Bind b) v))) (ex2 nat
+(\lambda (j: nat).(eq nat O (S j))) (\lambda (j: nat).(getl j e (CHead e
+(Bind b) v)))) (conj (eq nat O O) (eq C (CHead e (Bind b) v) (CHead e (Bind
+b) v)) (refl_equal nat O) (refl_equal C (CHead e (Bind b) v)))) d
+(clear_gen_bind b e d v (getl_gen_O (CHead e (Bind b) v) d H)))) (\lambda (n:
+nat).(\lambda (_: (((getl n (CHead e (Bind b) v) d) \to (or (land (eq nat n
+O) (eq C d (CHead e (Bind b) v))) (ex2 nat (\lambda (j: nat).(eq nat n (S
+j))) (\lambda (j: nat).(getl j e d))))))).(\lambda (H0: (getl (S n) (CHead e
+(Bind b) v) d)).(or_intror (land (eq nat (S n) O) (eq C d (CHead e (Bind b)
+v))) (ex2 nat (\lambda (j: nat).(eq nat (S n) (S j))) (\lambda (j: nat).(getl
+j e d))) (ex_intro2 nat (\lambda (j: nat).(eq nat (S n) (S j))) (\lambda (j:
+nat).(getl j e d)) n (refl_equal nat (S n)) (getl_gen_S (Bind b) e d v n
+H0)))))) i))))).
+
projects / helm.git / blobdiff