(* This file was automatically generated: do not edit *********************)
+include "LambdaDelta-1/nf2/props.ma".
-
-include "nf2/props.ma".
-
-include "drop1/defs.ma".
+include "LambdaDelta-1/drop1/fwd.ma".
theorem nf2_lift1:
\forall (e: C).(\forall (hds: PList).(\forall (c: C).(\forall (t: T).((drop1
\lambda (e: C).(\lambda (hds: PList).(PList_ind (\lambda (p: PList).(\forall
(c: C).(\forall (t: T).((drop1 p c e) \to ((nf2 e t) \to (nf2 c (lift1 p
t))))))) (\lambda (c: C).(\lambda (t: T).(\lambda (H: (drop1 PNil c
-e)).(\lambda (H0: (nf2 e t)).(let H1 \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 (nf2 c
-t)))))))) with [(drop1_nil c0) \Rightarrow (\lambda (_: (eq PList PNil
-PNil)).(\lambda (H2: (eq C c0 c)).(\lambda (H3: (eq C c0 e)).(eq_ind C c
-(\lambda (c1: C).((eq C c1 e) \to (nf2 c t))) (\lambda (H4: (eq C c
-e)).(eq_ind C e (\lambda (c1: C).(nf2 c1 t)) H0 c (sym_eq C c e H4))) c0
-(sym_eq C c0 c H2) H3)))) | (drop1_cons c1 c2 h d H1 c3 hds0 H2) \Rightarrow
-(\lambda (H3: (eq PList (PCons h d hds0) PNil)).(\lambda (H4: (eq C c1
-c)).(\lambda (H5: (eq C c3 e)).((let H6 \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 H3) in
-(False_ind ((eq C c1 c) \to ((eq C c3 e) \to ((drop h d c1 c2) \to ((drop1
-hds0 c2 c3) \to (nf2 c t))))) H6)) H4 H5 H1 H2))))]) in (H1 (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 (t:
-T).((drop1 p c e) \to ((nf2 e t) \to (nf2 c (lift1 p t)))))))).(\lambda (c:
-C).(\lambda (t: T).(\lambda (H0: (drop1 (PCons n n0 p) c e)).(\lambda (H1:
-(nf2 e t)).(let H2 \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 (nf2 c (lift n
-n0 (lift1 p t)))))))))) with [(drop1_nil c0) \Rightarrow (\lambda (H2: (eq
-PList PNil (PCons n n0 p))).(\lambda (H3: (eq C c0 c)).(\lambda (H4: (eq C c0
-e)).((let H5 \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) H2) in (False_ind ((eq C c0 c) \to ((eq
-C c0 e) \to (nf2 c (lift n n0 (lift1 p t))))) H5)) H3 H4)))) | (drop1_cons c1
-c2 h d H2 c3 hds0 H3) \Rightarrow (\lambda (H4: (eq PList (PCons h d hds0)
-(PCons n n0 p))).(\lambda (H5: (eq C c1 c)).(\lambda (H6: (eq C c3 e)).((let
-H7 \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) H4) in ((let H8 \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) H4) in ((let H9 \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) H4) 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 (nf2 c (lift n n0 (lift1 p t)))))))))) (\lambda
-(H10: (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 (nf2 c (lift n n0 (lift1 p t))))))))) (\lambda (H11: (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 (nf2 c (lift n n0 (lift1 p
-t)))))))) (\lambda (H12: (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 (nf2 c (lift n n0 (lift1 p
-t))))))) (\lambda (H13: (eq C c3 e)).(eq_ind C e (\lambda (c0: C).((drop n n0
-c c2) \to ((drop1 p c2 c0) \to (nf2 c (lift n n0 (lift1 p t)))))) (\lambda
-(H14: (drop n n0 c c2)).(\lambda (H15: (drop1 p c2 e)).(nf2_lift c2 (lift1 p
-t) (H c2 t H15 H1) c n n0 H14))) c3 (sym_eq C c3 e H13))) c1 (sym_eq C c1 c
-H12))) hds0 (sym_eq PList hds0 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 c) (refl_equal C e))))))))))) hds)).
+e)).(\lambda (H0: (nf2 e t)).(let H_y \def (drop1_gen_pnil c e H) in
+(eq_ind_r C e (\lambda (c0: C).(nf2 c0 t)) H0 c H_y)))))) (\lambda (n:
+nat).(\lambda (n0: nat).(\lambda (p: PList).(\lambda (H: ((\forall (c:
+C).(\forall (t: T).((drop1 p c e) \to ((nf2 e t) \to (nf2 c (lift1 p
+t)))))))).(\lambda (c: C).(\lambda (t: T).(\lambda (H0: (drop1 (PCons n n0 p)
+c e)).(\lambda (H1: (nf2 e t)).(let H_x \def (drop1_gen_pcons c e p n n0 H0)
+in (let H2 \def H_x in (ex2_ind C (\lambda (c2: C).(drop n n0 c c2)) (\lambda
+(c2: C).(drop1 p c2 e)) (nf2 c (lift n n0 (lift1 p t))) (\lambda (x:
+C).(\lambda (H3: (drop n n0 c x)).(\lambda (H4: (drop1 p x e)).(nf2_lift x
+(lift1 p t) (H x t H4 H1) c n n0 H3)))) H2))))))))))) hds)).
projects / helm.git / blobdiff