+++ /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/csubc/arity.ma".
-
-include "Basic-1/csubc/getl.ma".
-
-include "Basic-1/csubc/drop1.ma".
-
-include "Basic-1/csubc/props.ma".
-
-theorem sc3_arity_csubc:
- \forall (g: G).(\forall (c1: C).(\forall (t: T).(\forall (a: A).((arity g c1
-t a) \to (\forall (d1: C).(\forall (is: PList).((drop1 is d1 c1) \to (\forall
-(c2: C).((csubc g d1 c2) \to (sc3 g a c2 (lift1 is t)))))))))))
-\def
- \lambda (g: G).(\lambda (c1: C).(\lambda (t: T).(\lambda (a: A).(\lambda (H:
-(arity g c1 t a)).(arity_ind g (\lambda (c: C).(\lambda (t0: T).(\lambda (a0:
-A).(\forall (d1: C).(\forall (is: PList).((drop1 is d1 c) \to (\forall (c2:
-C).((csubc g d1 c2) \to (sc3 g a0 c2 (lift1 is t0)))))))))) (\lambda (c:
-C).(\lambda (n: nat).(\lambda (d1: C).(\lambda (is: PList).(\lambda (_:
-(drop1 is d1 c)).(\lambda (c2: C).(\lambda (_: (csubc g d1 c2)).(eq_ind_r T
-(TSort n) (\lambda (t0: T).(land (arity g c2 t0 (ASort O n)) (sn3 c2 t0)))
-(conj (arity g c2 (TSort n) (ASort O n)) (sn3 c2 (TSort n)) (arity_sort g c2
-n) (sn3_nf2 c2 (TSort n) (nf2_sort c2 n))) (lift1 is (TSort n)) (lift1_sort n
-is))))))))) (\lambda (c: C).(\lambda (d: C).(\lambda (u: T).(\lambda (i:
-nat).(\lambda (H0: (getl i c (CHead d (Bind Abbr) u))).(\lambda (a0:
-A).(\lambda (_: (arity g d u a0)).(\lambda (H2: ((\forall (d1: C).(\forall
-(is: PList).((drop1 is d1 d) \to (\forall (c2: C).((csubc g d1 c2) \to (sc3 g
-a0 c2 (lift1 is u))))))))).(\lambda (d1: C).(\lambda (is: PList).(\lambda
-(H3: (drop1 is d1 c)).(\lambda (c2: C).(\lambda (H4: (csubc g d1 c2)).(let
-H_x \def (drop1_getl_trans is c d1 H3 Abbr d u i H0) in (let H5 \def H_x in
-(ex2_ind C (\lambda (e2: C).(drop1 (ptrans is i) e2 d)) (\lambda (e2:
-C).(getl (trans is i) d1 (CHead e2 (Bind Abbr) (lift1 (ptrans is i) u))))
-(sc3 g a0 c2 (lift1 is (TLRef i))) (\lambda (x: C).(\lambda (_: (drop1
-(ptrans is i) x d)).(\lambda (H7: (getl (trans is i) d1 (CHead x (Bind Abbr)
-(lift1 (ptrans is i) u)))).(let H_x0 \def (csubc_getl_conf g d1 (CHead x
-(Bind Abbr) (lift1 (ptrans is i) u)) (trans is i) H7 c2 H4) in (let H8 \def
-H_x0 in (ex2_ind C (\lambda (e2: C).(getl (trans is i) c2 e2)) (\lambda (e2:
-C).(csubc g (CHead x (Bind Abbr) (lift1 (ptrans is i) u)) e2)) (sc3 g a0 c2
-(lift1 is (TLRef i))) (\lambda (x0: C).(\lambda (H9: (getl (trans is i) c2
-x0)).(\lambda (H10: (csubc g (CHead x (Bind Abbr) (lift1 (ptrans is i) u))
-x0)).(let H_x1 \def (csubc_gen_head_l g x x0 (lift1 (ptrans is i) u) (Bind
-Abbr) H10) in (let H11 \def H_x1 in (or3_ind (ex2 C (\lambda (c3: C).(eq C x0
-(CHead c3 (Bind Abbr) (lift1 (ptrans is i) u)))) (\lambda (c3: C).(csubc g x
-c3))) (ex5_3 C T A (\lambda (_: C).(\lambda (_: T).(\lambda (_: A).(eq K
-(Bind Abbr) (Bind Abst))))) (\lambda (c3: C).(\lambda (w: T).(\lambda (_:
-A).(eq C x0 (CHead c3 (Bind Abbr) w))))) (\lambda (c3: C).(\lambda (_:
-T).(\lambda (_: A).(csubc g x c3)))) (\lambda (_: C).(\lambda (_: T).(\lambda
-(a1: A).(sc3 g (asucc g a1) x (lift1 (ptrans is i) u))))) (\lambda (c3:
-C).(\lambda (w: T).(\lambda (a1: A).(sc3 g a1 c3 w))))) (ex4_3 B C T (\lambda
-(b: B).(\lambda (c3: C).(\lambda (v2: T).(eq C x0 (CHead c3 (Bind b) v2)))))
-(\lambda (_: B).(\lambda (_: C).(\lambda (_: T).(eq K (Bind Abbr) (Bind
-Void))))) (\lambda (b: B).(\lambda (_: C).(\lambda (_: T).(not (eq B b
-Void))))) (\lambda (_: B).(\lambda (c3: C).(\lambda (_: T).(csubc g x c3)))))
-(sc3 g a0 c2 (lift1 is (TLRef i))) (\lambda (H12: (ex2 C (\lambda (c3: C).(eq
-C x0 (CHead c3 (Bind Abbr) (lift1 (ptrans is i) u)))) (\lambda (c3: C).(csubc
-g x c3)))).(ex2_ind C (\lambda (c3: C).(eq C x0 (CHead c3 (Bind Abbr) (lift1
-(ptrans is i) u)))) (\lambda (c3: C).(csubc g x c3)) (sc3 g a0 c2 (lift1 is
-(TLRef i))) (\lambda (x1: C).(\lambda (H13: (eq C x0 (CHead x1 (Bind Abbr)
-(lift1 (ptrans is i) u)))).(\lambda (_: (csubc g x x1)).(let H15 \def (eq_ind
-C x0 (\lambda (c0: C).(getl (trans is i) c2 c0)) H9 (CHead x1 (Bind Abbr)
-(lift1 (ptrans is i) u)) H13) in (let H_y \def (sc3_abbr g a0 TNil) in
-(eq_ind_r T (TLRef (trans is i)) (\lambda (t0: T).(sc3 g a0 c2 t0)) (H_y
-(trans is i) x1 (lift1 (ptrans is i) u) c2 (eq_ind T (lift1 is (lift (S i) O
-u)) (\lambda (t0: T).(sc3 g a0 c2 t0)) (eq_ind T (lift1 (PConsTail is (S i)
-O) u) (\lambda (t0: T).(sc3 g a0 c2 t0)) (H2 d1 (PConsTail is (S i) O)
-(drop1_cons_tail c d (S i) O (getl_drop Abbr c d u i H0) is d1 H3) c2 H4)
-(lift1 is (lift (S i) O u)) (lift1_cons_tail u (S i) O is)) (lift (S (trans
-is i)) O (lift1 (ptrans is i) u)) (lift1_free is i u)) H15) (lift1 is (TLRef
-i)) (lift1_lref is i))))))) H12)) (\lambda (H12: (ex5_3 C T A (\lambda (_:
-C).(\lambda (_: T).(\lambda (_: A).(eq K (Bind Abbr) (Bind Abst))))) (\lambda
-(c3: C).(\lambda (w: T).(\lambda (_: A).(eq C x0 (CHead c3 (Bind Abbr) w)))))
-(\lambda (c3: C).(\lambda (_: T).(\lambda (_: A).(csubc g x c3)))) (\lambda
-(_: C).(\lambda (_: T).(\lambda (a1: A).(sc3 g (asucc g a1) x (lift1 (ptrans
-is i) u))))) (\lambda (c3: C).(\lambda (w: T).(\lambda (a1: A).(sc3 g a1 c3
-w)))))).(ex5_3_ind C T A (\lambda (_: C).(\lambda (_: T).(\lambda (_: A).(eq
-K (Bind Abbr) (Bind Abst))))) (\lambda (c3: C).(\lambda (w: T).(\lambda (_:
-A).(eq C x0 (CHead c3 (Bind Abbr) w))))) (\lambda (c3: C).(\lambda (_:
-T).(\lambda (_: A).(csubc g x c3)))) (\lambda (_: C).(\lambda (_: T).(\lambda
-(a1: A).(sc3 g (asucc g a1) x (lift1 (ptrans is i) u))))) (\lambda (c3:
-C).(\lambda (w: T).(\lambda (a1: A).(sc3 g a1 c3 w)))) (sc3 g a0 c2 (lift1 is
-(TLRef i))) (\lambda (x1: C).(\lambda (x2: T).(\lambda (x3: A).(\lambda (H13:
-(eq K (Bind Abbr) (Bind Abst))).(\lambda (H14: (eq C x0 (CHead x1 (Bind Abbr)
-x2))).(\lambda (_: (csubc g x x1)).(\lambda (_: (sc3 g (asucc g x3) x (lift1
-(ptrans is i) u))).(\lambda (_: (sc3 g x3 x1 x2)).(let H18 \def (eq_ind C x0
-(\lambda (c0: C).(getl (trans is i) c2 c0)) H9 (CHead x1 (Bind Abbr) x2) H14)
-in (let H19 \def (eq_ind K (Bind Abbr) (\lambda (ee: K).(match ee in K return
-(\lambda (_: K).Prop) with [(Bind b) \Rightarrow (match b in B return
-(\lambda (_: B).Prop) with [Abbr \Rightarrow True | Abst \Rightarrow False |
-Void \Rightarrow False]) | (Flat _) \Rightarrow False])) I (Bind Abst) H13)
-in (False_ind (sc3 g a0 c2 (lift1 is (TLRef i))) H19))))))))))) H12))
-(\lambda (H12: (ex4_3 B C T (\lambda (b: B).(\lambda (c3: C).(\lambda (v2:
-T).(eq C x0 (CHead c3 (Bind b) v2))))) (\lambda (_: B).(\lambda (_:
-C).(\lambda (_: T).(eq K (Bind Abbr) (Bind Void))))) (\lambda (b: B).(\lambda
-(_: C).(\lambda (_: T).(not (eq B b Void))))) (\lambda (_: B).(\lambda (c3:
-C).(\lambda (_: T).(csubc g x c3)))))).(ex4_3_ind B C T (\lambda (b:
-B).(\lambda (c3: C).(\lambda (v2: T).(eq C x0 (CHead c3 (Bind b) v2)))))
-(\lambda (_: B).(\lambda (_: C).(\lambda (_: T).(eq K (Bind Abbr) (Bind
-Void))))) (\lambda (b: B).(\lambda (_: C).(\lambda (_: T).(not (eq B b
-Void))))) (\lambda (_: B).(\lambda (c3: C).(\lambda (_: T).(csubc g x c3))))
-(sc3 g a0 c2 (lift1 is (TLRef i))) (\lambda (x1: B).(\lambda (x2: C).(\lambda
-(x3: T).(\lambda (H13: (eq C x0 (CHead x2 (Bind x1) x3))).(\lambda (H14: (eq
-K (Bind Abbr) (Bind Void))).(\lambda (_: (not (eq B x1 Void))).(\lambda (_:
-(csubc g x x2)).(let H17 \def (eq_ind C x0 (\lambda (c0: C).(getl (trans is
-i) c2 c0)) H9 (CHead x2 (Bind x1) x3) H13) in (let H18 \def (eq_ind K (Bind
-Abbr) (\lambda (ee: K).(match ee in K return (\lambda (_: K).Prop) with
-[(Bind b) \Rightarrow (match b in B return (\lambda (_: B).Prop) with [Abbr
-\Rightarrow True | Abst \Rightarrow False | Void \Rightarrow False]) | (Flat
-_) \Rightarrow False])) I (Bind Void) H14) in (False_ind (sc3 g a0 c2 (lift1
-is (TLRef i))) H18)))))))))) H12)) H11)))))) H8)))))) H5))))))))))))))))
-(\lambda (c: C).(\lambda (d: C).(\lambda (u: T).(\lambda (i: nat).(\lambda
-(H0: (getl i c (CHead d (Bind Abst) u))).(\lambda (a0: A).(\lambda (H1:
-(arity g d u (asucc g a0))).(\lambda (_: ((\forall (d1: C).(\forall (is:
-PList).((drop1 is d1 d) \to (\forall (c2: C).((csubc g d1 c2) \to (sc3 g
-(asucc g a0) c2 (lift1 is u))))))))).(\lambda (d1: C).(\lambda (is:
-PList).(\lambda (H3: (drop1 is d1 c)).(\lambda (c2: C).(\lambda (H4: (csubc g
-d1 c2)).(let H5 \def H0 in (let H_x \def (drop1_getl_trans is c d1 H3 Abst d
-u i H5) in (let H6 \def H_x in (ex2_ind C (\lambda (e2: C).(drop1 (ptrans is
-i) e2 d)) (\lambda (e2: C).(getl (trans is i) d1 (CHead e2 (Bind Abst) (lift1
-(ptrans is i) u)))) (sc3 g a0 c2 (lift1 is (TLRef i))) (\lambda (x:
-C).(\lambda (H7: (drop1 (ptrans is i) x d)).(\lambda (H8: (getl (trans is i)
-d1 (CHead x (Bind Abst) (lift1 (ptrans is i) u)))).(let H_x0 \def
-(csubc_getl_conf g d1 (CHead x (Bind Abst) (lift1 (ptrans is i) u)) (trans is
-i) H8 c2 H4) in (let H9 \def H_x0 in (ex2_ind C (\lambda (e2: C).(getl (trans
-is i) c2 e2)) (\lambda (e2: C).(csubc g (CHead x (Bind Abst) (lift1 (ptrans
-is i) u)) e2)) (sc3 g a0 c2 (lift1 is (TLRef i))) (\lambda (x0: C).(\lambda
-(H10: (getl (trans is i) c2 x0)).(\lambda (H11: (csubc g (CHead x (Bind Abst)
-(lift1 (ptrans is i) u)) x0)).(let H_x1 \def (csubc_gen_head_l g x x0 (lift1
-(ptrans is i) u) (Bind Abst) H11) in (let H12 \def H_x1 in (or3_ind (ex2 C
-(\lambda (c3: C).(eq C x0 (CHead c3 (Bind Abst) (lift1 (ptrans is i) u))))
-(\lambda (c3: C).(csubc g x c3))) (ex5_3 C T A (\lambda (_: C).(\lambda (_:
-T).(\lambda (_: A).(eq K (Bind Abst) (Bind Abst))))) (\lambda (c3:
-C).(\lambda (w: T).(\lambda (_: A).(eq C x0 (CHead c3 (Bind Abbr) w)))))
-(\lambda (c3: C).(\lambda (_: T).(\lambda (_: A).(csubc g x c3)))) (\lambda
-(_: C).(\lambda (_: T).(\lambda (a1: A).(sc3 g (asucc g a1) x (lift1 (ptrans
-is i) u))))) (\lambda (c3: C).(\lambda (w: T).(\lambda (a1: A).(sc3 g a1 c3
-w))))) (ex4_3 B C T (\lambda (b: B).(\lambda (c3: C).(\lambda (v2: T).(eq C
-x0 (CHead c3 (Bind b) v2))))) (\lambda (_: B).(\lambda (_: C).(\lambda (_:
-T).(eq K (Bind Abst) (Bind Void))))) (\lambda (b: B).(\lambda (_: C).(\lambda
-(_: T).(not (eq B b Void))))) (\lambda (_: B).(\lambda (c3: C).(\lambda (_:
-T).(csubc g x c3))))) (sc3 g a0 c2 (lift1 is (TLRef i))) (\lambda (H13: (ex2
-C (\lambda (c3: C).(eq C x0 (CHead c3 (Bind Abst) (lift1 (ptrans is i) u))))
-(\lambda (c3: C).(csubc g x c3)))).(ex2_ind C (\lambda (c3: C).(eq C x0
-(CHead c3 (Bind Abst) (lift1 (ptrans is i) u)))) (\lambda (c3: C).(csubc g x
-c3)) (sc3 g a0 c2 (lift1 is (TLRef i))) (\lambda (x1: C).(\lambda (H14: (eq C
-x0 (CHead x1 (Bind Abst) (lift1 (ptrans is i) u)))).(\lambda (_: (csubc g x
-x1)).(let H16 \def (eq_ind C x0 (\lambda (c0: C).(getl (trans is i) c2 c0))
-H10 (CHead x1 (Bind Abst) (lift1 (ptrans is i) u)) H14) in (let H_y \def
-(sc3_abst g a0 TNil) in (eq_ind_r T (TLRef (trans is i)) (\lambda (t0:
-T).(sc3 g a0 c2 t0)) (H_y c2 (trans is i) (csubc_arity_conf g d1 c2 H4 (TLRef
-(trans is i)) a0 (eq_ind T (lift1 is (TLRef i)) (\lambda (t0: T).(arity g d1
-t0 a0)) (arity_lift1 g a0 c is d1 (TLRef i) H3 (arity_abst g c d u i H0 a0
-H1)) (TLRef (trans is i)) (lift1_lref is i))) (nf2_lref_abst c2 x1 (lift1
-(ptrans is i) u) (trans is i) H16) I) (lift1 is (TLRef i)) (lift1_lref is
-i))))))) H13)) (\lambda (H13: (ex5_3 C T A (\lambda (_: C).(\lambda (_:
-T).(\lambda (_: A).(eq K (Bind Abst) (Bind Abst))))) (\lambda (c3:
-C).(\lambda (w: T).(\lambda (_: A).(eq C x0 (CHead c3 (Bind Abbr) w)))))
-(\lambda (c3: C).(\lambda (_: T).(\lambda (_: A).(csubc g x c3)))) (\lambda
-(_: C).(\lambda (_: T).(\lambda (a1: A).(sc3 g (asucc g a1) x (lift1 (ptrans
-is i) u))))) (\lambda (c3: C).(\lambda (w: T).(\lambda (a1: A).(sc3 g a1 c3
-w)))))).(ex5_3_ind C T A (\lambda (_: C).(\lambda (_: T).(\lambda (_: A).(eq
-K (Bind Abst) (Bind Abst))))) (\lambda (c3: C).(\lambda (w: T).(\lambda (_:
-A).(eq C x0 (CHead c3 (Bind Abbr) w))))) (\lambda (c3: C).(\lambda (_:
-T).(\lambda (_: A).(csubc g x c3)))) (\lambda (_: C).(\lambda (_: T).(\lambda
-(a1: A).(sc3 g (asucc g a1) x (lift1 (ptrans is i) u))))) (\lambda (c3:
-C).(\lambda (w: T).(\lambda (a1: A).(sc3 g a1 c3 w)))) (sc3 g a0 c2 (lift1 is
-(TLRef i))) (\lambda (x1: C).(\lambda (x2: T).(\lambda (x3: A).(\lambda (_:
-(eq K (Bind Abst) (Bind Abst))).(\lambda (H15: (eq C x0 (CHead x1 (Bind Abbr)
-x2))).(\lambda (_: (csubc g x x1)).(\lambda (H17: (sc3 g (asucc g x3) x
-(lift1 (ptrans is i) u))).(\lambda (H18: (sc3 g x3 x1 x2)).(let H19 \def
-(eq_ind C x0 (\lambda (c0: C).(getl (trans is i) c2 c0)) H10 (CHead x1 (Bind
-Abbr) x2) H15) in (let H_y \def (sc3_abbr g a0 TNil) in (eq_ind_r T (TLRef
-(trans is i)) (\lambda (t0: T).(sc3 g a0 c2 t0)) (H_y (trans is i) x1 x2 c2
-(let H_y0 \def (arity_lift1 g (asucc g a0) d (ptrans is i) x u H7 H1) in (let
-H_y1 \def (sc3_arity_gen g x (lift1 (ptrans is i) u) (asucc g x3) H17) in
-(sc3_repl g x3 c2 (lift (S (trans is i)) O x2) (sc3_lift g x3 x1 x2 H18 c2 (S
-(trans is i)) O (getl_drop Abbr c2 x1 x2 (trans is i) H19)) a0 (asucc_inj g
-x3 a0 (arity_mono g x (lift1 (ptrans is i) u) (asucc g x3) H_y1 (asucc g a0)
-H_y0))))) H19) (lift1 is (TLRef i)) (lift1_lref is i)))))))))))) H13))
-(\lambda (H13: (ex4_3 B C T (\lambda (b: B).(\lambda (c3: C).(\lambda (v2:
-T).(eq C x0 (CHead c3 (Bind b) v2))))) (\lambda (_: B).(\lambda (_:
-C).(\lambda (_: T).(eq K (Bind Abst) (Bind Void))))) (\lambda (b: B).(\lambda
-(_: C).(\lambda (_: T).(not (eq B b Void))))) (\lambda (_: B).(\lambda (c3:
-C).(\lambda (_: T).(csubc g x c3)))))).(ex4_3_ind B C T (\lambda (b:
-B).(\lambda (c3: C).(\lambda (v2: T).(eq C x0 (CHead c3 (Bind b) v2)))))
-(\lambda (_: B).(\lambda (_: C).(\lambda (_: T).(eq K (Bind Abst) (Bind
-Void))))) (\lambda (b: B).(\lambda (_: C).(\lambda (_: T).(not (eq B b
-Void))))) (\lambda (_: B).(\lambda (c3: C).(\lambda (_: T).(csubc g x c3))))
-(sc3 g a0 c2 (lift1 is (TLRef i))) (\lambda (x1: B).(\lambda (x2: C).(\lambda
-(x3: T).(\lambda (H14: (eq C x0 (CHead x2 (Bind x1) x3))).(\lambda (H15: (eq
-K (Bind Abst) (Bind Void))).(\lambda (_: (not (eq B x1 Void))).(\lambda (_:
-(csubc g x x2)).(let H18 \def (eq_ind C x0 (\lambda (c0: C).(getl (trans is
-i) c2 c0)) H10 (CHead x2 (Bind x1) x3) H14) in (let H19 \def (eq_ind K (Bind
-Abst) (\lambda (ee: K).(match ee in K return (\lambda (_: K).Prop) with
-[(Bind b) \Rightarrow (match b in B return (\lambda (_: B).Prop) with [Abbr
-\Rightarrow False | Abst \Rightarrow True | Void \Rightarrow False]) | (Flat
-_) \Rightarrow False])) I (Bind Void) H15) in (False_ind (sc3 g a0 c2 (lift1
-is (TLRef i))) H19)))))))))) H13)) H12)))))) H9)))))) H6)))))))))))))))))
-(\lambda (b: B).(\lambda (H0: (not (eq B b Abst))).(\lambda (c: C).(\lambda
-(u: T).(\lambda (a1: A).(\lambda (_: (arity g c u a1)).(\lambda (H2:
-((\forall (d1: C).(\forall (is: PList).((drop1 is d1 c) \to (\forall (c2:
-C).((csubc g d1 c2) \to (sc3 g a1 c2 (lift1 is u))))))))).(\lambda (t0:
-T).(\lambda (a2: A).(\lambda (_: (arity g (CHead c (Bind b) u) t0
-a2)).(\lambda (H4: ((\forall (d1: C).(\forall (is: PList).((drop1 is d1
-(CHead c (Bind b) u)) \to (\forall (c2: C).((csubc g d1 c2) \to (sc3 g a2 c2
-(lift1 is t0))))))))).(\lambda (d1: C).(\lambda (is: PList).(\lambda (H5:
-(drop1 is d1 c)).(\lambda (c2: C).(\lambda (H6: (csubc g d1 c2)).(let H_y
-\def (sc3_bind g b H0 a1 a2 TNil) in (eq_ind_r T (THead (Bind b) (lift1 is u)
-(lift1 (Ss is) t0)) (\lambda (t1: T).(sc3 g a2 c2 t1)) (H_y c2 (lift1 is u)
-(lift1 (Ss is) t0) (H4 (CHead d1 (Bind b) (lift1 is u)) (Ss is)
-(drop1_skip_bind b c is d1 u H5) (CHead c2 (Bind b) (lift1 is u)) (csubc_head
-g d1 c2 H6 (Bind b) (lift1 is u))) (H2 d1 is H5 c2 H6)) (lift1 is (THead
-(Bind b) u t0)) (lift1_bind b is u t0))))))))))))))))))) (\lambda (c:
-C).(\lambda (u: T).(\lambda (a1: A).(\lambda (H0: (arity g c u (asucc g
-a1))).(\lambda (H1: ((\forall (d1: C).(\forall (is: PList).((drop1 is d1 c)
-\to (\forall (c2: C).((csubc g d1 c2) \to (sc3 g (asucc g a1) c2 (lift1 is
-u))))))))).(\lambda (t0: T).(\lambda (a2: A).(\lambda (H2: (arity g (CHead c
-(Bind Abst) u) t0 a2)).(\lambda (H3: ((\forall (d1: C).(\forall (is:
-PList).((drop1 is d1 (CHead c (Bind Abst) u)) \to (\forall (c2: C).((csubc g
-d1 c2) \to (sc3 g a2 c2 (lift1 is t0))))))))).(\lambda (d1: C).(\lambda (is:
-PList).(\lambda (H4: (drop1 is d1 c)).(\lambda (c2: C).(\lambda (H5: (csubc g
-d1 c2)).(eq_ind_r T (THead (Bind Abst) (lift1 is u) (lift1 (Ss is) t0))
-(\lambda (t1: T).(land (arity g c2 t1 (AHead a1 a2)) (\forall (d: C).(\forall
-(w: T).((sc3 g a1 d w) \to (\forall (is0: PList).((drop1 is0 d c2) \to (sc3 g
-a2 d (THead (Flat Appl) w (lift1 is0 t1)))))))))) (conj (arity g c2 (THead
-(Bind Abst) (lift1 is u) (lift1 (Ss is) t0)) (AHead a1 a2)) (\forall (d:
-C).(\forall (w: T).((sc3 g a1 d w) \to (\forall (is0: PList).((drop1 is0 d
-c2) \to (sc3 g a2 d (THead (Flat Appl) w (lift1 is0 (THead (Bind Abst) (lift1
-is u) (lift1 (Ss is) t0)))))))))) (csubc_arity_conf g d1 c2 H5 (THead (Bind
-Abst) (lift1 is u) (lift1 (Ss is) t0)) (AHead a1 a2) (arity_head g d1 (lift1
-is u) a1 (arity_lift1 g (asucc g a1) c is d1 u H4 H0) (lift1 (Ss is) t0) a2
-(arity_lift1 g a2 (CHead c (Bind Abst) u) (Ss is) (CHead d1 (Bind Abst)
-(lift1 is u)) t0 (drop1_skip_bind Abst c is d1 u H4) H2))) (\lambda (d:
-C).(\lambda (w: T).(\lambda (H6: (sc3 g a1 d w)).(\lambda (is0:
-PList).(\lambda (H7: (drop1 is0 d c2)).(eq_ind_r T (THead (Bind Abst) (lift1
-is0 (lift1 is u)) (lift1 (Ss is0) (lift1 (Ss is) t0))) (\lambda (t1: T).(sc3
-g a2 d (THead (Flat Appl) w t1))) (let H8 \def (sc3_appl g a1 a2 TNil) in (H8
-d w (lift1 (Ss is0) (lift1 (Ss is) t0)) (let H_y \def (sc3_bind g Abbr
-(\lambda (H9: (eq B Abbr Abst)).(not_abbr_abst H9)) a1 a2 TNil) in (H_y d w
-(lift1 (Ss is0) (lift1 (Ss is) t0)) (let H_x \def (csubc_drop1_conf_rev g is0
-d c2 H7 d1 H5) in (let H9 \def H_x in (ex2_ind C (\lambda (c3: C).(drop1 is0
-c3 d1)) (\lambda (c3: C).(csubc g c3 d)) (sc3 g a2 (CHead d (Bind Abbr) w)
-(lift1 (Ss is0) (lift1 (Ss is) t0))) (\lambda (x: C).(\lambda (H10: (drop1
-is0 x d1)).(\lambda (H11: (csubc g x d)).(eq_ind_r T (lift1 (papp (Ss is0)
-(Ss is)) t0) (\lambda (t1: T).(sc3 g a2 (CHead d (Bind Abbr) w) t1))
-(eq_ind_r PList (Ss (papp is0 is)) (\lambda (p: PList).(sc3 g a2 (CHead d
-(Bind Abbr) w) (lift1 p t0))) (H3 (CHead x (Bind Abst) (lift1 (papp is0 is)
-u)) (Ss (papp is0 is)) (drop1_skip_bind Abst c (papp is0 is) x u (drop1_trans
-is0 x d1 H10 is c H4)) (CHead d (Bind Abbr) w) (csubc_abst g x d H11 (lift1
-(papp is0 is) u) a1 (H1 x (papp is0 is) (drop1_trans is0 x d1 H10 is c H4) x
-(csubc_refl g x)) w H6)) (papp (Ss is0) (Ss is)) (papp_ss is0 is)) (lift1 (Ss
-is0) (lift1 (Ss is) t0)) (lift1_lift1 (Ss is0) (Ss is) t0))))) H9))) H6)) H6
-(lift1 is0 (lift1 is u)) (sc3_lift1 g c2 (asucc g a1) is0 d (lift1 is u) (H1
-d1 is H4 c2 H5) H7))) (lift1 is0 (THead (Bind Abst) (lift1 is u) (lift1 (Ss
-is) t0))) (lift1_bind Abst is0 (lift1 is u) (lift1 (Ss is) t0))))))))) (lift1
-is (THead (Bind Abst) u t0)) (lift1_bind Abst is u t0))))))))))))))))
-(\lambda (c: C).(\lambda (u: T).(\lambda (a1: A).(\lambda (_: (arity g c u
-a1)).(\lambda (H1: ((\forall (d1: C).(\forall (is: PList).((drop1 is d1 c)
-\to (\forall (c2: C).((csubc g d1 c2) \to (sc3 g a1 c2 (lift1 is
-u))))))))).(\lambda (t0: T).(\lambda (a2: A).(\lambda (_: (arity g c t0
-(AHead a1 a2))).(\lambda (H3: ((\forall (d1: C).(\forall (is: PList).((drop1
-is d1 c) \to (\forall (c2: C).((csubc g d1 c2) \to (sc3 g (AHead a1 a2) c2
-(lift1 is t0))))))))).(\lambda (d1: C).(\lambda (is: PList).(\lambda (H4:
-(drop1 is d1 c)).(\lambda (c2: C).(\lambda (H5: (csubc g d1 c2)).(let H_y
-\def (H1 d1 is H4 c2 H5) in (let H_y0 \def (H3 d1 is H4 c2 H5) in (let H6
-\def H_y0 in (land_ind (arity g c2 (lift1 is t0) (AHead a1 a2)) (\forall (d:
-C).(\forall (w: T).((sc3 g a1 d w) \to (\forall (is0: PList).((drop1 is0 d
-c2) \to (sc3 g a2 d (THead (Flat Appl) w (lift1 is0 (lift1 is t0)))))))))
-(sc3 g a2 c2 (lift1 is (THead (Flat Appl) u t0))) (\lambda (_: (arity g c2
-(lift1 is t0) (AHead a1 a2))).(\lambda (H8: ((\forall (d: C).(\forall (w:
-T).((sc3 g a1 d w) \to (\forall (is0: PList).((drop1 is0 d c2) \to (sc3 g a2
-d (THead (Flat Appl) w (lift1 is0 (lift1 is t0))))))))))).(let H_y1 \def (H8
-c2 (lift1 is u) H_y PNil) in (eq_ind_r T (THead (Flat Appl) (lift1 is u)
-(lift1 is t0)) (\lambda (t1: T).(sc3 g a2 c2 t1)) (H_y1 (drop1_nil c2))
-(lift1 is (THead (Flat Appl) u t0)) (lift1_flat Appl is u t0)))))
-H6)))))))))))))))))) (\lambda (c: C).(\lambda (u: T).(\lambda (a0:
-A).(\lambda (_: (arity g c u (asucc g a0))).(\lambda (H1: ((\forall (d1:
-C).(\forall (is: PList).((drop1 is d1 c) \to (\forall (c2: C).((csubc g d1
-c2) \to (sc3 g (asucc g a0) c2 (lift1 is u))))))))).(\lambda (t0: T).(\lambda
-(_: (arity g c t0 a0)).(\lambda (H3: ((\forall (d1: C).(\forall (is:
-PList).((drop1 is d1 c) \to (\forall (c2: C).((csubc g d1 c2) \to (sc3 g a0
-c2 (lift1 is t0))))))))).(\lambda (d1: C).(\lambda (is: PList).(\lambda (H4:
-(drop1 is d1 c)).(\lambda (c2: C).(\lambda (H5: (csubc g d1 c2)).(let H_y
-\def (sc3_cast g a0 TNil) in (eq_ind_r T (THead (Flat Cast) (lift1 is u)
-(lift1 is t0)) (\lambda (t1: T).(sc3 g a0 c2 t1)) (H_y c2 (lift1 is u) (H1 d1
-is H4 c2 H5) (lift1 is t0) (H3 d1 is H4 c2 H5)) (lift1 is (THead (Flat Cast)
-u t0)) (lift1_flat Cast is u t0)))))))))))))))) (\lambda (c: C).(\lambda (t0:
-T).(\lambda (a1: A).(\lambda (_: (arity g c t0 a1)).(\lambda (H1: ((\forall
-(d1: C).(\forall (is: PList).((drop1 is d1 c) \to (\forall (c2: C).((csubc g
-d1 c2) \to (sc3 g a1 c2 (lift1 is t0))))))))).(\lambda (a2: A).(\lambda (H2:
-(leq g a1 a2)).(\lambda (d1: C).(\lambda (is: PList).(\lambda (H3: (drop1 is
-d1 c)).(\lambda (c2: C).(\lambda (H4: (csubc g d1 c2)).(sc3_repl g a1 c2
-(lift1 is t0) (H1 d1 is H3 c2 H4) a2 H2))))))))))))) c1 t a H))))).
-(* COMMENTS
-Initial nodes: 5940
-END *)
-
-theorem sc3_arity:
- \forall (g: G).(\forall (c: C).(\forall (t: T).(\forall (a: A).((arity g c t
-a) \to (sc3 g a c t)))))
-\def
- \lambda (g: G).(\lambda (c: C).(\lambda (t: T).(\lambda (a: A).(\lambda (H:
-(arity g c t a)).(let H_y \def (sc3_arity_csubc g c t a H c PNil) in (H_y
-(drop1_nil c) c (csubc_refl g c))))))).
-(* COMMENTS
-Initial nodes: 47
-END *)
-
projects / helm.git / blobdiff