(* This file was automatically generated: do not edit *********************)
-set "baseuri" "cic:/matita/LAMBDA-TYPES/LambdaDelta-1/drop1/props".
+include "LambdaDelta-1/drop1/fwd.ma".
-include "drop1/defs.ma".
+include "LambdaDelta-1/drop/props.ma".
-include "drop/props.ma".
-
-include "getl/defs.ma".
+include "LambdaDelta-1/getl/defs.ma".
theorem drop1_skip_bind:
\forall (b: B).(\forall (e: C).(\forall (hds: PList).(\forall (c:
\lambda (b: B).(\lambda (e: C).(\lambda (hds: PList).(PList_ind (\lambda (p:
PList).(\forall (c: C).(\forall (u: T).((drop1 p c e) \to (drop1 (Ss p)
(CHead c (Bind b) (lift1 p u)) (CHead e (Bind b) u)))))) (\lambda (c:
-C).(\lambda (u: T).(\lambda (H: (drop1 PNil c e)).(let H0 \def (match H in
-drop1 return (\lambda (p: PList).(\lambda (c0: C).(\lambda (c1: C).(\lambda
-(_: (drop1 p c0 c1)).((eq PList p PNil) \to ((eq C c0 c) \to ((eq C c1 e) \to
-(drop1 PNil (CHead c (Bind b) u) (CHead e (Bind b) u))))))))) with
-[(drop1_nil c0) \Rightarrow (\lambda (_: (eq PList PNil PNil)).(\lambda (H1:
-(eq C c0 c)).(\lambda (H2: (eq C c0 e)).(eq_ind C c (\lambda (c1: C).((eq C
-c1 e) \to (drop1 PNil (CHead c (Bind b) u) (CHead e (Bind b) u)))) (\lambda
-(H3: (eq C c e)).(eq_ind C e (\lambda (c1: C).(drop1 PNil (CHead c1 (Bind b)
-u) (CHead e (Bind b) u))) (drop1_nil (CHead e (Bind b) u)) c (sym_eq C c e
-H3))) c0 (sym_eq C c0 c H1) H2)))) | (drop1_cons c1 c2 h d H0 c3 hds0 H1)
-\Rightarrow (\lambda (H2: (eq PList (PCons h d hds0) PNil)).(\lambda (H3: (eq
-C c1 c)).(\lambda (H4: (eq C c3 e)).((let H5 \def (eq_ind PList (PCons h d
-hds0) (\lambda (e0: PList).(match e0 in PList return (\lambda (_:
-PList).Prop) with [PNil \Rightarrow False | (PCons _ _ _) \Rightarrow True]))
-I PNil H2) in (False_ind ((eq C c1 c) \to ((eq C c3 e) \to ((drop h d c1 c2)
-\to ((drop1 hds0 c2 c3) \to (drop1 PNil (CHead c (Bind b) u) (CHead e (Bind
-b) u)))))) H5)) H3 H4 H0 H1))))]) in (H0 (refl_equal PList PNil) (refl_equal
-C c) (refl_equal C e)))))) (\lambda (n: nat).(\lambda (n0: nat).(\lambda (p:
-PList).(\lambda (H: ((\forall (c: C).(\forall (u: T).((drop1 p c e) \to
-(drop1 (Ss p) (CHead c (Bind b) (lift1 p u)) (CHead e (Bind b)
-u))))))).(\lambda (c: C).(\lambda (u: T).(\lambda (H0: (drop1 (PCons n n0 p)
-c e)).(let H1 \def (match H0 in drop1 return (\lambda (p0: PList).(\lambda
-(c0: C).(\lambda (c1: C).(\lambda (_: (drop1 p0 c0 c1)).((eq PList p0 (PCons
-n n0 p)) \to ((eq C c0 c) \to ((eq C c1 e) \to (drop1 (PCons n (S n0) (Ss p))
-(CHead c (Bind b) (lift n n0 (lift1 p u))) (CHead e (Bind b) u))))))))) with
-[(drop1_nil c0) \Rightarrow (\lambda (H1: (eq PList PNil (PCons n n0
-p))).(\lambda (H2: (eq C c0 c)).(\lambda (H3: (eq C c0 e)).((let H4 \def
-(eq_ind PList PNil (\lambda (e0: PList).(match e0 in PList return (\lambda
-(_: PList).Prop) with [PNil \Rightarrow True | (PCons _ _ _) \Rightarrow
-False])) I (PCons n n0 p) H1) in (False_ind ((eq C c0 c) \to ((eq C c0 e) \to
-(drop1 (PCons n (S n0) (Ss p)) (CHead c (Bind b) (lift n n0 (lift1 p u)))
-(CHead e (Bind b) u)))) H4)) H2 H3)))) | (drop1_cons c1 c2 h d H1 c3 hds0 H2)
-\Rightarrow (\lambda (H3: (eq PList (PCons h d hds0) (PCons n n0
-p))).(\lambda (H4: (eq C c1 c)).(\lambda (H5: (eq C c3 e)).((let H6 \def
-(f_equal PList PList (\lambda (e0: PList).(match e0 in PList return (\lambda
-(_: PList).PList) with [PNil \Rightarrow hds0 | (PCons _ _ p0) \Rightarrow
-p0])) (PCons h d hds0) (PCons n n0 p) H3) in ((let H7 \def (f_equal PList nat
-(\lambda (e0: PList).(match e0 in PList return (\lambda (_: PList).nat) with
-[PNil \Rightarrow d | (PCons _ n1 _) \Rightarrow n1])) (PCons h d hds0)
-(PCons n n0 p) H3) in ((let H8 \def (f_equal PList nat (\lambda (e0:
-PList).(match e0 in PList return (\lambda (_: PList).nat) with [PNil
-\Rightarrow h | (PCons n1 _ _) \Rightarrow n1])) (PCons h d hds0) (PCons n n0
-p) H3) in (eq_ind nat n (\lambda (n1: nat).((eq nat d n0) \to ((eq PList hds0
-p) \to ((eq C c1 c) \to ((eq C c3 e) \to ((drop n1 d c1 c2) \to ((drop1 hds0
-c2 c3) \to (drop1 (PCons n (S n0) (Ss p)) (CHead c (Bind b) (lift n n0 (lift1
-p u))) (CHead e (Bind b) u))))))))) (\lambda (H9: (eq nat d n0)).(eq_ind nat
-n0 (\lambda (n1: nat).((eq PList hds0 p) \to ((eq C c1 c) \to ((eq C c3 e)
-\to ((drop n n1 c1 c2) \to ((drop1 hds0 c2 c3) \to (drop1 (PCons n (S n0) (Ss
-p)) (CHead c (Bind b) (lift n n0 (lift1 p u))) (CHead e (Bind b) u))))))))
-(\lambda (H10: (eq PList hds0 p)).(eq_ind PList p (\lambda (p0: PList).((eq C
-c1 c) \to ((eq C c3 e) \to ((drop n n0 c1 c2) \to ((drop1 p0 c2 c3) \to
-(drop1 (PCons n (S n0) (Ss p)) (CHead c (Bind b) (lift n n0 (lift1 p u)))
-(CHead e (Bind b) u))))))) (\lambda (H11: (eq C c1 c)).(eq_ind C c (\lambda
-(c0: C).((eq C c3 e) \to ((drop n n0 c0 c2) \to ((drop1 p c2 c3) \to (drop1
-(PCons n (S n0) (Ss p)) (CHead c (Bind b) (lift n n0 (lift1 p u))) (CHead e
-(Bind b) u)))))) (\lambda (H12: (eq C c3 e)).(eq_ind C e (\lambda (c0:
-C).((drop n n0 c c2) \to ((drop1 p c2 c0) \to (drop1 (PCons n (S n0) (Ss p))
-(CHead c (Bind b) (lift n n0 (lift1 p u))) (CHead e (Bind b) u))))) (\lambda
-(H13: (drop n n0 c c2)).(\lambda (H14: (drop1 p c2 e)).(drop1_cons (CHead c
-(Bind b) (lift n n0 (lift1 p u))) (CHead c2 (Bind b) (lift1 p u)) n (S n0)
-(drop_skip_bind n n0 c c2 H13 b (lift1 p u)) (CHead e (Bind b) u) (Ss p) (H
-c2 u H14)))) c3 (sym_eq C c3 e H12))) c1 (sym_eq C c1 c H11))) hds0 (sym_eq
-PList hds0 p H10))) d (sym_eq nat d n0 H9))) h (sym_eq nat h n H8))) H7))
-H6)) H4 H5 H1 H2))))]) in (H1 (refl_equal PList (PCons n n0 p)) (refl_equal C
-c) (refl_equal C e)))))))))) hds))).
+C).(\lambda (u: T).(\lambda (H: (drop1 PNil c e)).(let H_y \def
+(drop1_gen_pnil c e H) in (eq_ind_r C e (\lambda (c0: C).(drop1 PNil (CHead
+c0 (Bind b) u) (CHead e (Bind b) u))) (drop1_nil (CHead e (Bind b) u)) c
+H_y))))) (\lambda (n: nat).(\lambda (n0: nat).(\lambda (p: PList).(\lambda
+(H: ((\forall (c: C).(\forall (u: T).((drop1 p c e) \to (drop1 (Ss p) (CHead
+c (Bind b) (lift1 p u)) (CHead e (Bind b) u))))))).(\lambda (c: C).(\lambda
+(u: T).(\lambda (H0: (drop1 (PCons n n0 p) c e)).(let H_x \def
+(drop1_gen_pcons c e p n n0 H0) in (let H1 \def H_x in (ex2_ind C (\lambda
+(c2: C).(drop n n0 c c2)) (\lambda (c2: C).(drop1 p c2 e)) (drop1 (PCons n (S
+n0) (Ss p)) (CHead c (Bind b) (lift n n0 (lift1 p u))) (CHead e (Bind b) u))
+(\lambda (x: C).(\lambda (H2: (drop n n0 c x)).(\lambda (H3: (drop1 p x
+e)).(drop1_cons (CHead c (Bind b) (lift n n0 (lift1 p u))) (CHead x (Bind b)
+(lift1 p u)) n (S n0) (drop_skip_bind n n0 c x H2 b (lift1 p u)) (CHead e
+(Bind b) u) (Ss p) (H x u H3))))) H1)))))))))) hds))).
theorem drop1_cons_tail:
\forall (c2: C).(\forall (c3: C).(\forall (h: nat).(\forall (d: nat).((drop
\lambda (c2: C).(\lambda (c3: C).(\lambda (h: nat).(\lambda (d:
nat).(\lambda (H: (drop h d c2 c3)).(\lambda (hds: PList).(PList_ind (\lambda
(p: PList).(\forall (c1: C).((drop1 p c1 c2) \to (drop1 (PConsTail p h d) c1
-c3)))) (\lambda (c1: C).(\lambda (H0: (drop1 PNil c1 c2)).(let H1 \def (match
-H0 in drop1 return (\lambda (p: PList).(\lambda (c: C).(\lambda (c0:
-C).(\lambda (_: (drop1 p c c0)).((eq PList p PNil) \to ((eq C c c1) \to ((eq
-C c0 c2) \to (drop1 (PCons h d PNil) c1 c3)))))))) with [(drop1_nil c)
-\Rightarrow (\lambda (_: (eq PList PNil PNil)).(\lambda (H2: (eq C c
-c1)).(\lambda (H3: (eq C c c2)).(eq_ind C c1 (\lambda (c0: C).((eq C c0 c2)
-\to (drop1 (PCons h d PNil) c1 c3))) (\lambda (H4: (eq C c1 c2)).(eq_ind C c2
-(\lambda (c0: C).(drop1 (PCons h d PNil) c0 c3)) (drop1_cons c2 c3 h d H c3
-PNil (drop1_nil c3)) c1 (sym_eq C c1 c2 H4))) c (sym_eq C c c1 H2) H3)))) |
-(drop1_cons c0 c4 h0 d0 H1 c5 hds0 H2) \Rightarrow (\lambda (H3: (eq PList
-(PCons h0 d0 hds0) PNil)).(\lambda (H4: (eq C c0 c1)).(\lambda (H5: (eq C c5
-c2)).((let H6 \def (eq_ind PList (PCons h0 d0 hds0) (\lambda (e:
-PList).(match e in PList return (\lambda (_: PList).Prop) with [PNil
-\Rightarrow False | (PCons _ _ _) \Rightarrow True])) I PNil H3) in
-(False_ind ((eq C c0 c1) \to ((eq C c5 c2) \to ((drop h0 d0 c0 c4) \to
-((drop1 hds0 c4 c5) \to (drop1 (PCons h d PNil) c1 c3))))) H6)) H4 H5 H1
-H2))))]) in (H1 (refl_equal PList PNil) (refl_equal C c1) (refl_equal C
-c2))))) (\lambda (n: nat).(\lambda (n0: nat).(\lambda (p: PList).(\lambda
-(H0: ((\forall (c1: C).((drop1 p c1 c2) \to (drop1 (PConsTail p h d) c1
-c3))))).(\lambda (c1: C).(\lambda (H1: (drop1 (PCons n n0 p) c1 c2)).(let H2
-\def (match H1 in drop1 return (\lambda (p0: PList).(\lambda (c: C).(\lambda
-(c0: C).(\lambda (_: (drop1 p0 c c0)).((eq PList p0 (PCons n n0 p)) \to ((eq
-C c c1) \to ((eq C c0 c2) \to (drop1 (PCons n n0 (PConsTail p h d)) c1
-c3)))))))) with [(drop1_nil c) \Rightarrow (\lambda (H2: (eq PList PNil
-(PCons n n0 p))).(\lambda (H3: (eq C c c1)).(\lambda (H4: (eq C c c2)).((let
-H5 \def (eq_ind PList PNil (\lambda (e: PList).(match e in PList return
-(\lambda (_: PList).Prop) with [PNil \Rightarrow True | (PCons _ _ _)
-\Rightarrow False])) I (PCons n n0 p) H2) in (False_ind ((eq C c c1) \to ((eq
-C c c2) \to (drop1 (PCons n n0 (PConsTail p h d)) c1 c3))) H5)) H3 H4)))) |
-(drop1_cons c0 c4 h0 d0 H2 c5 hds0 H3) \Rightarrow (\lambda (H4: (eq PList
-(PCons h0 d0 hds0) (PCons n n0 p))).(\lambda (H5: (eq C c0 c1)).(\lambda (H6:
-(eq C c5 c2)).((let H7 \def (f_equal PList PList (\lambda (e: PList).(match e
-in PList return (\lambda (_: PList).PList) with [PNil \Rightarrow hds0 |
-(PCons _ _ p0) \Rightarrow p0])) (PCons h0 d0 hds0) (PCons n n0 p) H4) in
-((let H8 \def (f_equal PList nat (\lambda (e: PList).(match e in PList return
-(\lambda (_: PList).nat) with [PNil \Rightarrow d0 | (PCons _ n1 _)
-\Rightarrow n1])) (PCons h0 d0 hds0) (PCons n n0 p) H4) in ((let H9 \def
-(f_equal PList nat (\lambda (e: PList).(match e in PList return (\lambda (_:
-PList).nat) with [PNil \Rightarrow h0 | (PCons n1 _ _) \Rightarrow n1]))
-(PCons h0 d0 hds0) (PCons n n0 p) H4) in (eq_ind nat n (\lambda (n1:
-nat).((eq nat d0 n0) \to ((eq PList hds0 p) \to ((eq C c0 c1) \to ((eq C c5
-c2) \to ((drop n1 d0 c0 c4) \to ((drop1 hds0 c4 c5) \to (drop1 (PCons n n0
-(PConsTail p h d)) c1 c3)))))))) (\lambda (H10: (eq nat d0 n0)).(eq_ind nat
-n0 (\lambda (n1: nat).((eq PList hds0 p) \to ((eq C c0 c1) \to ((eq C c5 c2)
-\to ((drop n n1 c0 c4) \to ((drop1 hds0 c4 c5) \to (drop1 (PCons n n0
-(PConsTail p h d)) c1 c3))))))) (\lambda (H11: (eq PList hds0 p)).(eq_ind
-PList p (\lambda (p0: PList).((eq C c0 c1) \to ((eq C c5 c2) \to ((drop n n0
-c0 c4) \to ((drop1 p0 c4 c5) \to (drop1 (PCons n n0 (PConsTail p h d)) c1
-c3)))))) (\lambda (H12: (eq C c0 c1)).(eq_ind C c1 (\lambda (c: C).((eq C c5
-c2) \to ((drop n n0 c c4) \to ((drop1 p c4 c5) \to (drop1 (PCons n n0
-(PConsTail p h d)) c1 c3))))) (\lambda (H13: (eq C c5 c2)).(eq_ind C c2
-(\lambda (c: C).((drop n n0 c1 c4) \to ((drop1 p c4 c) \to (drop1 (PCons n n0
-(PConsTail p h d)) c1 c3)))) (\lambda (H14: (drop n n0 c1 c4)).(\lambda (H15:
-(drop1 p c4 c2)).(drop1_cons c1 c4 n n0 H14 c3 (PConsTail p h d) (H0 c4
-H15)))) c5 (sym_eq C c5 c2 H13))) c0 (sym_eq C c0 c1 H12))) hds0 (sym_eq
-PList hds0 p H11))) d0 (sym_eq nat d0 n0 H10))) h0 (sym_eq nat h0 n H9)))
-H8)) H7)) H5 H6 H2 H3))))]) in (H2 (refl_equal PList (PCons n n0 p))
-(refl_equal C c1) (refl_equal C c2))))))))) hds)))))).
+c3)))) (\lambda (c1: C).(\lambda (H0: (drop1 PNil c1 c2)).(let H_y \def
+(drop1_gen_pnil c1 c2 H0) in (eq_ind_r C c2 (\lambda (c: C).(drop1 (PCons h d
+PNil) c c3)) (drop1_cons c2 c3 h d H c3 PNil (drop1_nil c3)) c1 H_y))))
+(\lambda (n: nat).(\lambda (n0: nat).(\lambda (p: PList).(\lambda (H0:
+((\forall (c1: C).((drop1 p c1 c2) \to (drop1 (PConsTail p h d) c1
+c3))))).(\lambda (c1: C).(\lambda (H1: (drop1 (PCons n n0 p) c1 c2)).(let H_x
+\def (drop1_gen_pcons c1 c2 p n n0 H1) in (let H2 \def H_x in (ex2_ind C
+(\lambda (c4: C).(drop n n0 c1 c4)) (\lambda (c4: C).(drop1 p c4 c2)) (drop1
+(PCons n n0 (PConsTail p h d)) c1 c3) (\lambda (x: C).(\lambda (H3: (drop n
+n0 c1 x)).(\lambda (H4: (drop1 p x c2)).(drop1_cons c1 x n n0 H3 c3
+(PConsTail p h d) (H0 x H4))))) H2))))))))) hds)))))).
theorem drop1_trans:
\forall (is1: PList).(\forall (c1: C).(\forall (c0: C).((drop1 is1 c1 c0)
C).(\forall (c0: C).((drop1 p c1 c0) \to (\forall (is2: PList).(\forall (c2:
C).((drop1 is2 c0 c2) \to (drop1 (papp p is2) c1 c2)))))))) (\lambda (c1:
C).(\lambda (c0: C).(\lambda (H: (drop1 PNil c1 c0)).(\lambda (is2:
-PList).(\lambda (c2: C).(\lambda (H0: (drop1 is2 c0 c2)).(let H1 \def (match
-H in drop1 return (\lambda (p: PList).(\lambda (c: C).(\lambda (c3:
-C).(\lambda (_: (drop1 p c c3)).((eq PList p PNil) \to ((eq C c c1) \to ((eq
-C c3 c0) \to (drop1 is2 c1 c2)))))))) with [(drop1_nil c) \Rightarrow
-(\lambda (_: (eq PList PNil PNil)).(\lambda (H2: (eq C c c1)).(\lambda (H3:
-(eq C c c0)).(eq_ind C c1 (\lambda (c3: C).((eq C c3 c0) \to (drop1 is2 c1
-c2))) (\lambda (H4: (eq C c1 c0)).(eq_ind C c0 (\lambda (c3: C).(drop1 is2 c3
-c2)) (let H5 \def (eq_ind_r C c0 (\lambda (c3: C).(drop1 is2 c3 c2)) H0 c1
-H4) in (eq_ind C c1 (\lambda (c3: C).(drop1 is2 c3 c2)) H5 c0 H4)) c1 (sym_eq
-C c1 c0 H4))) c (sym_eq C c c1 H2) H3)))) | (drop1_cons c3 c4 h d H1 c5 hds
-H2) \Rightarrow (\lambda (H3: (eq PList (PCons h d hds) PNil)).(\lambda (H4:
-(eq C c3 c1)).(\lambda (H5: (eq C c5 c0)).((let H6 \def (eq_ind PList (PCons
-h d hds) (\lambda (e: PList).(match e in PList return (\lambda (_:
-PList).Prop) with [PNil \Rightarrow False | (PCons _ _ _) \Rightarrow True]))
-I PNil H3) in (False_ind ((eq C c3 c1) \to ((eq C c5 c0) \to ((drop h d c3
-c4) \to ((drop1 hds c4 c5) \to (drop1 is2 c1 c2))))) H6)) H4 H5 H1 H2))))])
-in (H1 (refl_equal PList PNil) (refl_equal C c1) (refl_equal C c0)))))))))
-(\lambda (n: nat).(\lambda (n0: nat).(\lambda (p: PList).(\lambda (H:
-((\forall (c1: C).(\forall (c0: C).((drop1 p c1 c0) \to (\forall (is2:
-PList).(\forall (c2: C).((drop1 is2 c0 c2) \to (drop1 (papp p is2) c1
-c2))))))))).(\lambda (c1: C).(\lambda (c0: C).(\lambda (H0: (drop1 (PCons n
-n0 p) c1 c0)).(\lambda (is2: PList).(\lambda (c2: C).(\lambda (H1: (drop1 is2
-c0 c2)).(let H2 \def (match H0 in drop1 return (\lambda (p0: PList).(\lambda
-(c: C).(\lambda (c3: C).(\lambda (_: (drop1 p0 c c3)).((eq PList p0 (PCons n
-n0 p)) \to ((eq C c c1) \to ((eq C c3 c0) \to (drop1 (PCons n n0 (papp p
-is2)) c1 c2)))))))) with [(drop1_nil c) \Rightarrow (\lambda (H2: (eq PList
-PNil (PCons n n0 p))).(\lambda (H3: (eq C c c1)).(\lambda (H4: (eq C c
-c0)).((let H5 \def (eq_ind PList PNil (\lambda (e: PList).(match e in PList
-return (\lambda (_: PList).Prop) with [PNil \Rightarrow True | (PCons _ _ _)
-\Rightarrow False])) I (PCons n n0 p) H2) in (False_ind ((eq C c c1) \to ((eq
-C c c0) \to (drop1 (PCons n n0 (papp p is2)) c1 c2))) H5)) H3 H4)))) |
-(drop1_cons c3 c4 h d H2 c5 hds H3) \Rightarrow (\lambda (H4: (eq PList
-(PCons h d hds) (PCons n n0 p))).(\lambda (H5: (eq C c3 c1)).(\lambda (H6:
-(eq C c5 c0)).((let H7 \def (f_equal PList PList (\lambda (e: PList).(match e
-in PList return (\lambda (_: PList).PList) with [PNil \Rightarrow hds |
-(PCons _ _ p0) \Rightarrow p0])) (PCons h d hds) (PCons n n0 p) H4) in ((let
-H8 \def (f_equal PList nat (\lambda (e: PList).(match e in PList return
-(\lambda (_: PList).nat) with [PNil \Rightarrow d | (PCons _ n1 _)
-\Rightarrow n1])) (PCons h d hds) (PCons n n0 p) H4) in ((let H9 \def
-(f_equal PList nat (\lambda (e: PList).(match e in PList return (\lambda (_:
-PList).nat) with [PNil \Rightarrow h | (PCons n1 _ _) \Rightarrow n1]))
-(PCons h d hds) (PCons n n0 p) H4) in (eq_ind nat n (\lambda (n1: nat).((eq
-nat d n0) \to ((eq PList hds p) \to ((eq C c3 c1) \to ((eq C c5 c0) \to
-((drop n1 d c3 c4) \to ((drop1 hds c4 c5) \to (drop1 (PCons n n0 (papp p
-is2)) c1 c2)))))))) (\lambda (H10: (eq nat d n0)).(eq_ind nat n0 (\lambda
-(n1: nat).((eq PList hds p) \to ((eq C c3 c1) \to ((eq C c5 c0) \to ((drop n
-n1 c3 c4) \to ((drop1 hds c4 c5) \to (drop1 (PCons n n0 (papp p is2)) c1
-c2))))))) (\lambda (H11: (eq PList hds p)).(eq_ind PList p (\lambda (p0:
-PList).((eq C c3 c1) \to ((eq C c5 c0) \to ((drop n n0 c3 c4) \to ((drop1 p0
-c4 c5) \to (drop1 (PCons n n0 (papp p is2)) c1 c2)))))) (\lambda (H12: (eq C
-c3 c1)).(eq_ind C c1 (\lambda (c: C).((eq C c5 c0) \to ((drop n n0 c c4) \to
-((drop1 p c4 c5) \to (drop1 (PCons n n0 (papp p is2)) c1 c2))))) (\lambda
-(H13: (eq C c5 c0)).(eq_ind C c0 (\lambda (c: C).((drop n n0 c1 c4) \to
-((drop1 p c4 c) \to (drop1 (PCons n n0 (papp p is2)) c1 c2)))) (\lambda (H14:
-(drop n n0 c1 c4)).(\lambda (H15: (drop1 p c4 c0)).(drop1_cons c1 c4 n n0 H14
-c2 (papp p is2) (H c4 c0 H15 is2 c2 H1)))) c5 (sym_eq C c5 c0 H13))) c3
-(sym_eq C c3 c1 H12))) hds (sym_eq PList hds p H11))) d (sym_eq nat d n0
-H10))) h (sym_eq nat h n H9))) H8)) H7)) H5 H6 H2 H3))))]) in (H2 (refl_equal
-PList (PCons n n0 p)) (refl_equal C c1) (refl_equal C c0))))))))))))) is1).
+PList).(\lambda (c2: C).(\lambda (H0: (drop1 is2 c0 c2)).(let H_y \def
+(drop1_gen_pnil c1 c0 H) in (let H1 \def (eq_ind_r C c0 (\lambda (c:
+C).(drop1 is2 c c2)) H0 c1 H_y) in H1)))))))) (\lambda (n: nat).(\lambda (n0:
+nat).(\lambda (p: PList).(\lambda (H: ((\forall (c1: C).(\forall (c0:
+C).((drop1 p c1 c0) \to (\forall (is2: PList).(\forall (c2: C).((drop1 is2 c0
+c2) \to (drop1 (papp p is2) c1 c2))))))))).(\lambda (c1: C).(\lambda (c0:
+C).(\lambda (H0: (drop1 (PCons n n0 p) c1 c0)).(\lambda (is2: PList).(\lambda
+(c2: C).(\lambda (H1: (drop1 is2 c0 c2)).(let H_x \def (drop1_gen_pcons c1 c0
+p n n0 H0) in (let H2 \def H_x in (ex2_ind C (\lambda (c3: C).(drop n n0 c1
+c3)) (\lambda (c3: C).(drop1 p c3 c0)) (drop1 (PCons n n0 (papp p is2)) c1
+c2) (\lambda (x: C).(\lambda (H3: (drop n n0 c1 x)).(\lambda (H4: (drop1 p x
+c0)).(drop1_cons c1 x n n0 H3 c2 (papp p is2) (H x c0 H4 is2 c2 H1)))))
+H2))))))))))))) is1).
projects / helm.git / blobdiff