+++ /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_1/drop1/defs.ma".
-
-implied rec lemma drop1_ind (P: (PList \to (C \to (C \to Prop)))) (f:
-(\forall (c: C).(P PNil c c))) (f0: (\forall (c1: C).(\forall (c2:
-C).(\forall (h: nat).(\forall (d: nat).((drop h d c1 c2) \to (\forall (c3:
-C).(\forall (hds: PList).((drop1 hds c2 c3) \to ((P hds c2 c3) \to (P (PCons
-h d hds) c1 c3))))))))))) (p: PList) (c: C) (c0: C) (d: drop1 p c c0) on d: P
-p c c0 \def match d with [(drop1_nil c1) \Rightarrow (f c1) | (drop1_cons c1
-c2 h d0 d1 c3 hds d2) \Rightarrow (f0 c1 c2 h d0 d1 c3 hds d2 ((drop1_ind P f
-f0) hds c2 c3 d2))].
-
-lemma drop1_gen_pnil:
- \forall (c1: C).(\forall (c2: C).((drop1 PNil c1 c2) \to (eq C c1 c2)))
-\def
- \lambda (c1: C).(\lambda (c2: C).(\lambda (H: (drop1 PNil c1 c2)).(insert_eq
-PList PNil (\lambda (p: PList).(drop1 p c1 c2)) (\lambda (_: PList).(eq C c1
-c2)) (\lambda (y: PList).(\lambda (H0: (drop1 y c1 c2)).(drop1_ind (\lambda
-(p: PList).(\lambda (c: C).(\lambda (c0: C).((eq PList p PNil) \to (eq C c
-c0))))) (\lambda (c: C).(\lambda (_: (eq PList PNil PNil)).(refl_equal C c)))
-(\lambda (c3: C).(\lambda (c4: C).(\lambda (h: nat).(\lambda (d:
-nat).(\lambda (_: (drop h d c3 c4)).(\lambda (c5: C).(\lambda (hds:
-PList).(\lambda (_: (drop1 hds c4 c5)).(\lambda (_: (((eq PList hds PNil) \to
-(eq C c4 c5)))).(\lambda (H4: (eq PList (PCons h d hds) PNil)).(let H5 \def
-(eq_ind PList (PCons h d hds) (\lambda (ee: PList).(match ee with [PNil
-\Rightarrow False | (PCons _ _ _) \Rightarrow True])) I PNil H4) in
-(False_ind (eq C c3 c5) H5)))))))))))) y c1 c2 H0))) H))).
-
-lemma drop1_gen_pcons:
- \forall (c1: C).(\forall (c3: C).(\forall (hds: PList).(\forall (h:
-nat).(\forall (d: nat).((drop1 (PCons h d hds) c1 c3) \to (ex2 C (\lambda
-(c2: C).(drop h d c1 c2)) (\lambda (c2: C).(drop1 hds c2 c3))))))))
-\def
- \lambda (c1: C).(\lambda (c3: C).(\lambda (hds: PList).(\lambda (h:
-nat).(\lambda (d: nat).(\lambda (H: (drop1 (PCons h d hds) c1 c3)).(insert_eq
-PList (PCons h d hds) (\lambda (p: PList).(drop1 p c1 c3)) (\lambda (_:
-PList).(ex2 C (\lambda (c2: C).(drop h d c1 c2)) (\lambda (c2: C).(drop1 hds
-c2 c3)))) (\lambda (y: PList).(\lambda (H0: (drop1 y c1 c3)).(drop1_ind
-(\lambda (p: PList).(\lambda (c: C).(\lambda (c0: C).((eq PList p (PCons h d
-hds)) \to (ex2 C (\lambda (c2: C).(drop h d c c2)) (\lambda (c2: C).(drop1
-hds c2 c0))))))) (\lambda (c: C).(\lambda (H1: (eq PList PNil (PCons h d
-hds))).(let H2 \def (eq_ind PList PNil (\lambda (ee: PList).(match ee with
-[PNil \Rightarrow True | (PCons _ _ _) \Rightarrow False])) I (PCons h d hds)
-H1) in (False_ind (ex2 C (\lambda (c2: C).(drop h d c c2)) (\lambda (c2:
-C).(drop1 hds c2 c))) H2)))) (\lambda (c2: C).(\lambda (c4: C).(\lambda (h0:
-nat).(\lambda (d0: nat).(\lambda (H1: (drop h0 d0 c2 c4)).(\lambda (c5:
-C).(\lambda (hds0: PList).(\lambda (H2: (drop1 hds0 c4 c5)).(\lambda (H3:
-(((eq PList hds0 (PCons h d hds)) \to (ex2 C (\lambda (c6: C).(drop h d c4
-c6)) (\lambda (c6: C).(drop1 hds c6 c5)))))).(\lambda (H4: (eq PList (PCons
-h0 d0 hds0) (PCons h d hds))).(let H5 \def (f_equal PList nat (\lambda (e:
-PList).(match e with [PNil \Rightarrow h0 | (PCons n _ _) \Rightarrow n]))
-(PCons h0 d0 hds0) (PCons h d hds) H4) in ((let H6 \def (f_equal PList nat
-(\lambda (e: PList).(match e with [PNil \Rightarrow d0 | (PCons _ n _)
-\Rightarrow n])) (PCons h0 d0 hds0) (PCons h d hds) H4) in ((let H7 \def
-(f_equal PList PList (\lambda (e: PList).(match e with [PNil \Rightarrow hds0
-| (PCons _ _ p) \Rightarrow p])) (PCons h0 d0 hds0) (PCons h d hds) H4) in
-(\lambda (H8: (eq nat d0 d)).(\lambda (H9: (eq nat h0 h)).(let H10 \def
-(eq_ind PList hds0 (\lambda (p: PList).((eq PList p (PCons h d hds)) \to (ex2
-C (\lambda (c6: C).(drop h d c4 c6)) (\lambda (c6: C).(drop1 hds c6 c5)))))
-H3 hds H7) in (let H11 \def (eq_ind PList hds0 (\lambda (p: PList).(drop1 p
-c4 c5)) H2 hds H7) in (let H12 \def (eq_ind nat d0 (\lambda (n: nat).(drop h0
-n c2 c4)) H1 d H8) in (let H13 \def (eq_ind nat h0 (\lambda (n: nat).(drop n
-d c2 c4)) H12 h H9) in (ex_intro2 C (\lambda (c6: C).(drop h d c2 c6))
-(\lambda (c6: C).(drop1 hds c6 c5)) c4 H13 H11)))))))) H6)) H5)))))))))))) y
-c1 c3 H0))) H)))))).
-
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