--- /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/csubc/drop.ma".
+
+theorem drop1_csubc_trans:
+ \forall (g: G).(\forall (hds: PList).(\forall (c2: C).(\forall (e2:
+C).((drop1 hds c2 e2) \to (\forall (e1: C).((csubc g e2 e1) \to (ex2 C
+(\lambda (c1: C).(drop1 hds c1 e1)) (\lambda (c1: C).(csubc g c2 c1)))))))))
+\def
+ \lambda (g: G).(\lambda (hds: PList).(PList_ind (\lambda (p: PList).(\forall
+(c2: C).(\forall (e2: C).((drop1 p c2 e2) \to (\forall (e1: C).((csubc g e2
+e1) \to (ex2 C (\lambda (c1: C).(drop1 p c1 e1)) (\lambda (c1: C).(csubc g c2
+c1))))))))) (\lambda (c2: C).(\lambda (e2: C).(\lambda (H: (drop1 PNil c2
+e2)).(\lambda (e1: C).(\lambda (H0: (csubc g e2 e1)).(let H_y \def
+(drop1_gen_pnil c2 e2 H) in (let H1 \def (eq_ind_r C e2 (\lambda (c:
+C).(csubc g c e1)) H0 c2 H_y) in (ex_intro2 C (\lambda (c1: C).(drop1 PNil c1
+e1)) (\lambda (c1: C).(csubc g c2 c1)) e1 (drop1_nil e1) H1)))))))) (\lambda
+(n: nat).(\lambda (n0: nat).(\lambda (p: PList).(\lambda (H: ((\forall (c2:
+C).(\forall (e2: C).((drop1 p c2 e2) \to (\forall (e1: C).((csubc g e2 e1)
+\to (ex2 C (\lambda (c1: C).(drop1 p c1 e1)) (\lambda (c1: C).(csubc g c2
+c1)))))))))).(\lambda (c2: C).(\lambda (e2: C).(\lambda (H0: (drop1 (PCons n
+n0 p) c2 e2)).(\lambda (e1: C).(\lambda (H1: (csubc g e2 e1)).(let H_x \def
+(drop1_gen_pcons c2 e2 p n n0 H0) in (let H2 \def H_x in (ex2_ind C (\lambda
+(c3: C).(drop n n0 c2 c3)) (\lambda (c3: C).(drop1 p c3 e2)) (ex2 C (\lambda
+(c1: C).(drop1 (PCons n n0 p) c1 e1)) (\lambda (c1: C).(csubc g c2 c1)))
+(\lambda (x: C).(\lambda (H3: (drop n n0 c2 x)).(\lambda (H4: (drop1 p x
+e2)).(let H_x0 \def (H x e2 H4 e1 H1) in (let H5 \def H_x0 in (ex2_ind C
+(\lambda (c1: C).(drop1 p c1 e1)) (\lambda (c1: C).(csubc g x c1)) (ex2 C
+(\lambda (c1: C).(drop1 (PCons n n0 p) c1 e1)) (\lambda (c1: C).(csubc g c2
+c1))) (\lambda (x0: C).(\lambda (H6: (drop1 p x0 e1)).(\lambda (H7: (csubc g
+x x0)).(let H_x1 \def (drop_csubc_trans g c2 x n0 n H3 x0 H7) in (let H8 \def
+H_x1 in (ex2_ind C (\lambda (c1: C).(drop n n0 c1 x0)) (\lambda (c1:
+C).(csubc g c2 c1)) (ex2 C (\lambda (c1: C).(drop1 (PCons n n0 p) c1 e1))
+(\lambda (c1: C).(csubc g c2 c1))) (\lambda (x1: C).(\lambda (H9: (drop n n0
+x1 x0)).(\lambda (H10: (csubc g c2 x1)).(ex_intro2 C (\lambda (c1: C).(drop1
+(PCons n n0 p) c1 e1)) (\lambda (c1: C).(csubc g c2 c1)) x1 (drop1_cons x1 x0
+n n0 H9 e1 p H6) H10)))) H8)))))) H5)))))) H2)))))))))))) hds)).
+
+theorem csubc_drop1_conf_rev:
+ \forall (g: G).(\forall (hds: PList).(\forall (c2: C).(\forall (e2:
+C).((drop1 hds c2 e2) \to (\forall (e1: C).((csubc g e1 e2) \to (ex2 C
+(\lambda (c1: C).(drop1 hds c1 e1)) (\lambda (c1: C).(csubc g c1 c2)))))))))
+\def
+ \lambda (g: G).(\lambda (hds: PList).(PList_ind (\lambda (p: PList).(\forall
+(c2: C).(\forall (e2: C).((drop1 p c2 e2) \to (\forall (e1: C).((csubc g e1
+e2) \to (ex2 C (\lambda (c1: C).(drop1 p c1 e1)) (\lambda (c1: C).(csubc g c1
+c2))))))))) (\lambda (c2: C).(\lambda (e2: C).(\lambda (H: (drop1 PNil c2
+e2)).(\lambda (e1: C).(\lambda (H0: (csubc g e1 e2)).(let H_y \def
+(drop1_gen_pnil c2 e2 H) in (let H1 \def (eq_ind_r C e2 (\lambda (c:
+C).(csubc g e1 c)) H0 c2 H_y) in (ex_intro2 C (\lambda (c1: C).(drop1 PNil c1
+e1)) (\lambda (c1: C).(csubc g c1 c2)) e1 (drop1_nil e1) H1)))))))) (\lambda
+(n: nat).(\lambda (n0: nat).(\lambda (p: PList).(\lambda (H: ((\forall (c2:
+C).(\forall (e2: C).((drop1 p c2 e2) \to (\forall (e1: C).((csubc g e1 e2)
+\to (ex2 C (\lambda (c1: C).(drop1 p c1 e1)) (\lambda (c1: C).(csubc g c1
+c2)))))))))).(\lambda (c2: C).(\lambda (e2: C).(\lambda (H0: (drop1 (PCons n
+n0 p) c2 e2)).(\lambda (e1: C).(\lambda (H1: (csubc g e1 e2)).(let H_x \def
+(drop1_gen_pcons c2 e2 p n n0 H0) in (let H2 \def H_x in (ex2_ind C (\lambda
+(c3: C).(drop n n0 c2 c3)) (\lambda (c3: C).(drop1 p c3 e2)) (ex2 C (\lambda
+(c1: C).(drop1 (PCons n n0 p) c1 e1)) (\lambda (c1: C).(csubc g c1 c2)))
+(\lambda (x: C).(\lambda (H3: (drop n n0 c2 x)).(\lambda (H4: (drop1 p x
+e2)).(let H_x0 \def (H x e2 H4 e1 H1) in (let H5 \def H_x0 in (ex2_ind C
+(\lambda (c1: C).(drop1 p c1 e1)) (\lambda (c1: C).(csubc g c1 x)) (ex2 C
+(\lambda (c1: C).(drop1 (PCons n n0 p) c1 e1)) (\lambda (c1: C).(csubc g c1
+c2))) (\lambda (x0: C).(\lambda (H6: (drop1 p x0 e1)).(\lambda (H7: (csubc g
+x0 x)).(let H_x1 \def (csubc_drop_conf_rev g c2 x n0 n H3 x0 H7) in (let H8
+\def H_x1 in (ex2_ind C (\lambda (c1: C).(drop n n0 c1 x0)) (\lambda (c1:
+C).(csubc g c1 c2)) (ex2 C (\lambda (c1: C).(drop1 (PCons n n0 p) c1 e1))
+(\lambda (c1: C).(csubc g c1 c2))) (\lambda (x1: C).(\lambda (H9: (drop n n0
+x1 x0)).(\lambda (H10: (csubc g x1 c2)).(ex_intro2 C (\lambda (c1: C).(drop1
+(PCons n n0 p) c1 e1)) (\lambda (c1: C).(csubc g c1 c2)) x1 (drop1_cons x1 x0
+n n0 H9 e1 p H6) H10)))) H8)))))) H5)))))) H2)))))))))))) hds)).
+
projects / helm.git / blobdiff