+++ /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/ty3/arity.ma".
-
-include "Basic-1/pc3/nf2.ma".
-
-include "Basic-1/nf2/arity.ma".
-
-definition ty3_nf2_inv_abst_premise:
- C \to (T \to (T \to Prop))
-\def
- \lambda (c: C).(\lambda (w: T).(\lambda (u: T).(\forall (d: C).(\forall (wi:
-T).(\forall (i: nat).((getl i c (CHead d (Bind Abst) wi)) \to (\forall (vs:
-TList).((pc3 c (THeads (Flat Appl) vs (lift (S i) O wi)) (THead (Bind Abst) w
-u)) \to False)))))))).
-
-theorem ty3_nf2_inv_abst_premise_csort:
- \forall (w: T).(\forall (u: T).(\forall (m: nat).(ty3_nf2_inv_abst_premise
-(CSort m) w u)))
-\def
- \lambda (w: T).(\lambda (u: T).(\lambda (m: nat).(\lambda (d: C).(\lambda
-(wi: T).(\lambda (i: nat).(\lambda (H: (getl i (CSort m) (CHead d (Bind Abst)
-wi))).(\lambda (vs: TList).(\lambda (_: (pc3 (CSort m) (THeads (Flat Appl) vs
-(lift (S i) O wi)) (THead (Bind Abst) w u))).(getl_gen_sort m i (CHead d
-(Bind Abst) wi) H False))))))))).
-(* COMMENTS
-Initial nodes: 85
-END *)
-
-theorem ty3_nf2_inv_all:
- \forall (g: G).(\forall (c: C).(\forall (t: T).(\forall (u: T).((ty3 g c t
-u) \to ((nf2 c t) \to (or3 (ex3_2 T T (\lambda (w: T).(\lambda (u0: T).(eq T
-t (THead (Bind Abst) w u0)))) (\lambda (w: T).(\lambda (_: T).(nf2 c w)))
-(\lambda (w: T).(\lambda (u0: T).(nf2 (CHead c (Bind Abst) w) u0)))) (ex nat
-(\lambda (n: nat).(eq T t (TSort n)))) (ex3_2 TList nat (\lambda (ws:
-TList).(\lambda (i: nat).(eq T t (THeads (Flat Appl) ws (TLRef i)))))
-(\lambda (ws: TList).(\lambda (_: nat).(nfs2 c ws))) (\lambda (_:
-TList).(\lambda (i: nat).(nf2 c (TLRef i)))))))))))
-\def
- \lambda (g: G).(\lambda (c: C).(\lambda (t: T).(\lambda (u: T).(\lambda (H:
-(ty3 g c t u)).(\lambda (H0: (nf2 c t)).(let H_x \def (ty3_arity g c t u H)
-in (let H1 \def H_x in (ex2_ind A (\lambda (a1: A).(arity g c t a1)) (\lambda
-(a1: A).(arity g c u (asucc g a1))) (or3 (ex3_2 T T (\lambda (w: T).(\lambda
-(u0: T).(eq T t (THead (Bind Abst) w u0)))) (\lambda (w: T).(\lambda (_:
-T).(nf2 c w))) (\lambda (w: T).(\lambda (u0: T).(nf2 (CHead c (Bind Abst) w)
-u0)))) (ex nat (\lambda (n: nat).(eq T t (TSort n)))) (ex3_2 TList nat
-(\lambda (ws: TList).(\lambda (i: nat).(eq T t (THeads (Flat Appl) ws (TLRef
-i))))) (\lambda (ws: TList).(\lambda (_: nat).(nfs2 c ws))) (\lambda (_:
-TList).(\lambda (i: nat).(nf2 c (TLRef i)))))) (\lambda (x: A).(\lambda (H2:
-(arity g c t x)).(\lambda (_: (arity g c u (asucc g x))).(arity_nf2_inv_all g
-c t x H2 H0)))) H1)))))))).
-(* COMMENTS
-Initial nodes: 233
-END *)
-
-theorem ty3_nf2_inv_sort:
- \forall (g: G).(\forall (c: C).(\forall (t: T).(\forall (m: nat).((ty3 g c t
-(TSort m)) \to ((nf2 c t) \to (or (ex2 nat (\lambda (n: nat).(eq T t (TSort
-n))) (\lambda (n: nat).(eq nat m (next g n)))) (ex3_2 TList nat (\lambda (ws:
-TList).(\lambda (i: nat).(eq T t (THeads (Flat Appl) ws (TLRef i)))))
-(\lambda (ws: TList).(\lambda (_: nat).(nfs2 c ws))) (\lambda (_:
-TList).(\lambda (i: nat).(nf2 c (TLRef i)))))))))))
-\def
- \lambda (g: G).(\lambda (c: C).(\lambda (t: T).(\lambda (m: nat).(\lambda
-(H: (ty3 g c t (TSort m))).(\lambda (H0: (nf2 c t)).(let H_x \def
-(ty3_nf2_inv_all g c t (TSort m) H H0) in (let H1 \def H_x in (or3_ind (ex3_2
-T T (\lambda (w: T).(\lambda (u: T).(eq T t (THead (Bind Abst) w u))))
-(\lambda (w: T).(\lambda (_: T).(nf2 c w))) (\lambda (w: T).(\lambda (u:
-T).(nf2 (CHead c (Bind Abst) w) u)))) (ex nat (\lambda (n: nat).(eq T t
-(TSort n)))) (ex3_2 TList nat (\lambda (ws: TList).(\lambda (i: nat).(eq T t
-(THeads (Flat Appl) ws (TLRef i))))) (\lambda (ws: TList).(\lambda (_:
-nat).(nfs2 c ws))) (\lambda (_: TList).(\lambda (i: nat).(nf2 c (TLRef i)))))
-(or (ex2 nat (\lambda (n: nat).(eq T t (TSort n))) (\lambda (n: nat).(eq nat
-m (next g n)))) (ex3_2 TList nat (\lambda (ws: TList).(\lambda (i: nat).(eq T
-t (THeads (Flat Appl) ws (TLRef i))))) (\lambda (ws: TList).(\lambda (_:
-nat).(nfs2 c ws))) (\lambda (_: TList).(\lambda (i: nat).(nf2 c (TLRef
-i)))))) (\lambda (H2: (ex3_2 T T (\lambda (w: T).(\lambda (u: T).(eq T t
-(THead (Bind Abst) w u)))) (\lambda (w: T).(\lambda (_: T).(nf2 c w)))
-(\lambda (w: T).(\lambda (u: T).(nf2 (CHead c (Bind Abst) w)
-u))))).(ex3_2_ind T T (\lambda (w: T).(\lambda (u: T).(eq T t (THead (Bind
-Abst) w u)))) (\lambda (w: T).(\lambda (_: T).(nf2 c w))) (\lambda (w:
-T).(\lambda (u: T).(nf2 (CHead c (Bind Abst) w) u))) (or (ex2 nat (\lambda
-(n: nat).(eq T t (TSort n))) (\lambda (n: nat).(eq nat m (next g n)))) (ex3_2
-TList nat (\lambda (ws: TList).(\lambda (i: nat).(eq T t (THeads (Flat Appl)
-ws (TLRef i))))) (\lambda (ws: TList).(\lambda (_: nat).(nfs2 c ws)))
-(\lambda (_: TList).(\lambda (i: nat).(nf2 c (TLRef i)))))) (\lambda (x0:
-T).(\lambda (x1: T).(\lambda (H3: (eq T t (THead (Bind Abst) x0
-x1))).(\lambda (_: (nf2 c x0)).(\lambda (_: (nf2 (CHead c (Bind Abst) x0)
-x1)).(let H6 \def (eq_ind T t (\lambda (t0: T).(ty3 g c t0 (TSort m))) H
-(THead (Bind Abst) x0 x1) H3) in (eq_ind_r T (THead (Bind Abst) x0 x1)
-(\lambda (t0: T).(or (ex2 nat (\lambda (n: nat).(eq T t0 (TSort n))) (\lambda
-(n: nat).(eq nat m (next g n)))) (ex3_2 TList nat (\lambda (ws:
-TList).(\lambda (i: nat).(eq T t0 (THeads (Flat Appl) ws (TLRef i)))))
-(\lambda (ws: TList).(\lambda (_: nat).(nfs2 c ws))) (\lambda (_:
-TList).(\lambda (i: nat).(nf2 c (TLRef i))))))) (ex3_2_ind T T (\lambda (t2:
-T).(\lambda (_: T).(pc3 c (THead (Bind Abst) x0 t2) (TSort m)))) (\lambda (_:
-T).(\lambda (t0: T).(ty3 g c x0 t0))) (\lambda (t2: T).(\lambda (_: T).(ty3 g
-(CHead c (Bind Abst) x0) x1 t2))) (or (ex2 nat (\lambda (n: nat).(eq T (THead
-(Bind Abst) x0 x1) (TSort n))) (\lambda (n: nat).(eq nat m (next g n))))
-(ex3_2 TList nat (\lambda (ws: TList).(\lambda (i: nat).(eq T (THead (Bind
-Abst) x0 x1) (THeads (Flat Appl) ws (TLRef i))))) (\lambda (ws:
-TList).(\lambda (_: nat).(nfs2 c ws))) (\lambda (_: TList).(\lambda (i:
-nat).(nf2 c (TLRef i)))))) (\lambda (x2: T).(\lambda (x3: T).(\lambda (H7:
-(pc3 c (THead (Bind Abst) x0 x2) (TSort m))).(\lambda (_: (ty3 g c x0
-x3)).(\lambda (_: (ty3 g (CHead c (Bind Abst) x0) x1 x2)).(pc3_gen_sort_abst
-c x0 x2 m (pc3_s c (TSort m) (THead (Bind Abst) x0 x2) H7) (or (ex2 nat
-(\lambda (n: nat).(eq T (THead (Bind Abst) x0 x1) (TSort n))) (\lambda (n:
-nat).(eq nat m (next g n)))) (ex3_2 TList nat (\lambda (ws: TList).(\lambda
-(i: nat).(eq T (THead (Bind Abst) x0 x1) (THeads (Flat Appl) ws (TLRef i)))))
-(\lambda (ws: TList).(\lambda (_: nat).(nfs2 c ws))) (\lambda (_:
-TList).(\lambda (i: nat).(nf2 c (TLRef i)))))))))))) (ty3_gen_bind g Abst c
-x0 x1 (TSort m) H6)) t H3))))))) H2)) (\lambda (H2: (ex nat (\lambda (n:
-nat).(eq T t (TSort n))))).(ex_ind nat (\lambda (n: nat).(eq T t (TSort n)))
-(or (ex2 nat (\lambda (n: nat).(eq T t (TSort n))) (\lambda (n: nat).(eq nat
-m (next g n)))) (ex3_2 TList nat (\lambda (ws: TList).(\lambda (i: nat).(eq T
-t (THeads (Flat Appl) ws (TLRef i))))) (\lambda (ws: TList).(\lambda (_:
-nat).(nfs2 c ws))) (\lambda (_: TList).(\lambda (i: nat).(nf2 c (TLRef
-i)))))) (\lambda (x: nat).(\lambda (H3: (eq T t (TSort x))).(let H4 \def
-(eq_ind T t (\lambda (t0: T).(ty3 g c t0 (TSort m))) H (TSort x) H3) in
-(eq_ind_r T (TSort x) (\lambda (t0: T).(or (ex2 nat (\lambda (n: nat).(eq T
-t0 (TSort n))) (\lambda (n: nat).(eq nat m (next g n)))) (ex3_2 TList nat
-(\lambda (ws: TList).(\lambda (i: nat).(eq T t0 (THeads (Flat Appl) ws (TLRef
-i))))) (\lambda (ws: TList).(\lambda (_: nat).(nfs2 c ws))) (\lambda (_:
-TList).(\lambda (i: nat).(nf2 c (TLRef i))))))) (eq_ind nat (next g x)
-(\lambda (n: nat).(or (ex2 nat (\lambda (n0: nat).(eq T (TSort x) (TSort
-n0))) (\lambda (n0: nat).(eq nat n (next g n0)))) (ex3_2 TList nat (\lambda
-(ws: TList).(\lambda (i: nat).(eq T (TSort x) (THeads (Flat Appl) ws (TLRef
-i))))) (\lambda (ws: TList).(\lambda (_: nat).(nfs2 c ws))) (\lambda (_:
-TList).(\lambda (i: nat).(nf2 c (TLRef i))))))) (or_introl (ex2 nat (\lambda
-(n: nat).(eq T (TSort x) (TSort n))) (\lambda (n: nat).(eq nat (next g x)
-(next g n)))) (ex3_2 TList nat (\lambda (ws: TList).(\lambda (i: nat).(eq T
-(TSort x) (THeads (Flat Appl) ws (TLRef i))))) (\lambda (ws: TList).(\lambda
-(_: nat).(nfs2 c ws))) (\lambda (_: TList).(\lambda (i: nat).(nf2 c (TLRef
-i))))) (ex_intro2 nat (\lambda (n: nat).(eq T (TSort x) (TSort n))) (\lambda
-(n: nat).(eq nat (next g x) (next g n))) x (refl_equal T (TSort x))
-(refl_equal nat (next g x)))) m (pc3_gen_sort c (next g x) m (ty3_gen_sort g
-c (TSort m) x H4))) t H3)))) H2)) (\lambda (H2: (ex3_2 TList nat (\lambda
-(ws: TList).(\lambda (i: nat).(eq T t (THeads (Flat Appl) ws (TLRef i)))))
-(\lambda (ws: TList).(\lambda (_: nat).(nfs2 c ws))) (\lambda (_:
-TList).(\lambda (i: nat).(nf2 c (TLRef i)))))).(ex3_2_ind TList nat (\lambda
-(ws: TList).(\lambda (i: nat).(eq T t (THeads (Flat Appl) ws (TLRef i)))))
-(\lambda (ws: TList).(\lambda (_: nat).(nfs2 c ws))) (\lambda (_:
-TList).(\lambda (i: nat).(nf2 c (TLRef i)))) (or (ex2 nat (\lambda (n:
-nat).(eq T t (TSort n))) (\lambda (n: nat).(eq nat m (next g n)))) (ex3_2
-TList nat (\lambda (ws: TList).(\lambda (i: nat).(eq T t (THeads (Flat Appl)
-ws (TLRef i))))) (\lambda (ws: TList).(\lambda (_: nat).(nfs2 c ws)))
-(\lambda (_: TList).(\lambda (i: nat).(nf2 c (TLRef i)))))) (\lambda (x0:
-TList).(\lambda (x1: nat).(\lambda (H3: (eq T t (THeads (Flat Appl) x0 (TLRef
-x1)))).(\lambda (H4: (nfs2 c x0)).(\lambda (H5: (nf2 c (TLRef x1))).(let H6
-\def (eq_ind T t (\lambda (t0: T).(ty3 g c t0 (TSort m))) H (THeads (Flat
-Appl) x0 (TLRef x1)) H3) in (eq_ind_r T (THeads (Flat Appl) x0 (TLRef x1))
-(\lambda (t0: T).(or (ex2 nat (\lambda (n: nat).(eq T t0 (TSort n))) (\lambda
-(n: nat).(eq nat m (next g n)))) (ex3_2 TList nat (\lambda (ws:
-TList).(\lambda (i: nat).(eq T t0 (THeads (Flat Appl) ws (TLRef i)))))
-(\lambda (ws: TList).(\lambda (_: nat).(nfs2 c ws))) (\lambda (_:
-TList).(\lambda (i: nat).(nf2 c (TLRef i))))))) (or_intror (ex2 nat (\lambda
-(n: nat).(eq T (THeads (Flat Appl) x0 (TLRef x1)) (TSort n))) (\lambda (n:
-nat).(eq nat m (next g n)))) (ex3_2 TList nat (\lambda (ws: TList).(\lambda
-(i: nat).(eq T (THeads (Flat Appl) x0 (TLRef x1)) (THeads (Flat Appl) ws
-(TLRef i))))) (\lambda (ws: TList).(\lambda (_: nat).(nfs2 c ws))) (\lambda
-(_: TList).(\lambda (i: nat).(nf2 c (TLRef i))))) (ex3_2_intro TList nat
-(\lambda (ws: TList).(\lambda (i: nat).(eq T (THeads (Flat Appl) x0 (TLRef
-x1)) (THeads (Flat Appl) ws (TLRef i))))) (\lambda (ws: TList).(\lambda (_:
-nat).(nfs2 c ws))) (\lambda (_: TList).(\lambda (i: nat).(nf2 c (TLRef i))))
-x0 x1 (refl_equal T (THeads (Flat Appl) x0 (TLRef x1))) H4 H5)) t H3)))))))
-H2)) H1)))))))).
-(* COMMENTS
-Initial nodes: 2045
-END *)
-
-theorem ty3_nf2_gen__ty3_nf2_inv_abst_aux:
- \forall (c: C).(\forall (w1: T).(\forall (u1: T).((ty3_nf2_inv_abst_premise
-c w1 u1) \to (\forall (t: T).(\forall (w2: T).(\forall (u2: T).((pc3 c (THead
-(Flat Appl) t (THead (Bind Abst) w2 u2)) (THead (Bind Abst) w1 u1)) \to
-(ty3_nf2_inv_abst_premise c w2 u2))))))))
-\def
- \lambda (c: C).(\lambda (w1: T).(\lambda (u1: T).(\lambda (H: ((\forall (d:
-C).(\forall (wi: T).(\forall (i: nat).((getl i c (CHead d (Bind Abst) wi))
-\to (\forall (vs: TList).((pc3 c (THeads (Flat Appl) vs (lift (S i) O wi))
-(THead (Bind Abst) w1 u1)) \to False)))))))).(\lambda (t: T).(\lambda (w2:
-T).(\lambda (u2: T).(\lambda (H0: (pc3 c (THead (Flat Appl) t (THead (Bind
-Abst) w2 u2)) (THead (Bind Abst) w1 u1))).(\lambda (d: C).(\lambda (wi:
-T).(\lambda (i: nat).(\lambda (H1: (getl i c (CHead d (Bind Abst)
-wi))).(\lambda (vs: TList).(\lambda (H2: (pc3 c (THeads (Flat Appl) vs (lift
-(S i) O wi)) (THead (Bind Abst) w2 u2))).(H d wi i H1 (TCons t vs) (pc3_t
-(THead (Flat Appl) t (THead (Bind Abst) w2 u2)) c (THead (Flat Appl) t
-(THeads (Flat Appl) vs (lift (S i) O wi))) (pc3_thin_dx c (THeads (Flat Appl)
-vs (lift (S i) O wi)) (THead (Bind Abst) w2 u2) H2 t Appl) (THead (Bind Abst)
-w1 u1) H0))))))))))))))).
-(* COMMENTS
-Initial nodes: 271
-END *)
-
-theorem ty3_nf2_inv_abst:
- \forall (g: G).(\forall (c: C).(\forall (t: T).(\forall (w: T).(\forall (u:
-T).((ty3 g c t (THead (Bind Abst) w u)) \to ((nf2 c t) \to ((nf2 c w) \to
-((ty3_nf2_inv_abst_premise c w u) \to (ex4_2 T T (\lambda (v: T).(\lambda (_:
-T).(eq T t (THead (Bind Abst) w v)))) (\lambda (_: T).(\lambda (w0: T).(ty3 g
-c w w0))) (\lambda (v: T).(\lambda (_: T).(ty3 g (CHead c (Bind Abst) w) v
-u))) (\lambda (v: T).(\lambda (_: T).(nf2 (CHead c (Bind Abst) w)
-v))))))))))))
-\def
- \lambda (g: G).(\lambda (c: C).(\lambda (t: T).(\lambda (w: T).(\lambda (u:
-T).(\lambda (H: (ty3 g c t (THead (Bind Abst) w u))).(\lambda (H0: (nf2 c
-t)).(\lambda (H1: (nf2 c w)).(\lambda (H2: (ty3_nf2_inv_abst_premise c w
-u)).(let H_x \def (ty3_nf2_inv_all g c t (THead (Bind Abst) w u) H H0) in
-(let H3 \def H_x in (or3_ind (ex3_2 T T (\lambda (w0: T).(\lambda (u0: T).(eq
-T t (THead (Bind Abst) w0 u0)))) (\lambda (w0: T).(\lambda (_: T).(nf2 c
-w0))) (\lambda (w0: T).(\lambda (u0: T).(nf2 (CHead c (Bind Abst) w0) u0))))
-(ex nat (\lambda (n: nat).(eq T t (TSort n)))) (ex3_2 TList nat (\lambda (ws:
-TList).(\lambda (i: nat).(eq T t (THeads (Flat Appl) ws (TLRef i)))))
-(\lambda (ws: TList).(\lambda (_: nat).(nfs2 c ws))) (\lambda (_:
-TList).(\lambda (i: nat).(nf2 c (TLRef i))))) (ex4_2 T T (\lambda (v:
-T).(\lambda (_: T).(eq T t (THead (Bind Abst) w v)))) (\lambda (_:
-T).(\lambda (w0: T).(ty3 g c w w0))) (\lambda (v: T).(\lambda (_: T).(ty3 g
-(CHead c (Bind Abst) w) v u))) (\lambda (v: T).(\lambda (_: T).(nf2 (CHead c
-(Bind Abst) w) v)))) (\lambda (H4: (ex3_2 T T (\lambda (w0: T).(\lambda (u0:
-T).(eq T t (THead (Bind Abst) w0 u0)))) (\lambda (w0: T).(\lambda (_: T).(nf2
-c w0))) (\lambda (w0: T).(\lambda (u0: T).(nf2 (CHead c (Bind Abst) w0)
-u0))))).(ex3_2_ind T T (\lambda (w0: T).(\lambda (u0: T).(eq T t (THead (Bind
-Abst) w0 u0)))) (\lambda (w0: T).(\lambda (_: T).(nf2 c w0))) (\lambda (w0:
-T).(\lambda (u0: T).(nf2 (CHead c (Bind Abst) w0) u0))) (ex4_2 T T (\lambda
-(v: T).(\lambda (_: T).(eq T t (THead (Bind Abst) w v)))) (\lambda (_:
-T).(\lambda (w0: T).(ty3 g c w w0))) (\lambda (v: T).(\lambda (_: T).(ty3 g
-(CHead c (Bind Abst) w) v u))) (\lambda (v: T).(\lambda (_: T).(nf2 (CHead c
-(Bind Abst) w) v)))) (\lambda (x0: T).(\lambda (x1: T).(\lambda (H5: (eq T t
-(THead (Bind Abst) x0 x1))).(\lambda (H6: (nf2 c x0)).(\lambda (H7: (nf2
-(CHead c (Bind Abst) x0) x1)).(let H8 \def (eq_ind T t (\lambda (t0: T).(ty3
-g c t0 (THead (Bind Abst) w u))) H (THead (Bind Abst) x0 x1) H5) in (eq_ind_r
-T (THead (Bind Abst) x0 x1) (\lambda (t0: T).(ex4_2 T T (\lambda (v:
-T).(\lambda (_: T).(eq T t0 (THead (Bind Abst) w v)))) (\lambda (_:
-T).(\lambda (w0: T).(ty3 g c w w0))) (\lambda (v: T).(\lambda (_: T).(ty3 g
-(CHead c (Bind Abst) w) v u))) (\lambda (v: T).(\lambda (_: T).(nf2 (CHead c
-(Bind Abst) w) v))))) (ex_ind T (\lambda (t0: T).(ty3 g c (THead (Bind Abst)
-w u) t0)) (ex4_2 T T (\lambda (v: T).(\lambda (_: T).(eq T (THead (Bind Abst)
-x0 x1) (THead (Bind Abst) w v)))) (\lambda (_: T).(\lambda (w0: T).(ty3 g c w
-w0))) (\lambda (v: T).(\lambda (_: T).(ty3 g (CHead c (Bind Abst) w) v u)))
-(\lambda (v: T).(\lambda (_: T).(nf2 (CHead c (Bind Abst) w) v)))) (\lambda
-(x: T).(\lambda (H9: (ty3 g c (THead (Bind Abst) w u) x)).(ex3_2_ind T T
-(\lambda (t2: T).(\lambda (_: T).(pc3 c (THead (Bind Abst) w t2) x)))
-(\lambda (_: T).(\lambda (t0: T).(ty3 g c w t0))) (\lambda (t2: T).(\lambda
-(_: T).(ty3 g (CHead c (Bind Abst) w) u t2))) (ex4_2 T T (\lambda (v:
-T).(\lambda (_: T).(eq T (THead (Bind Abst) x0 x1) (THead (Bind Abst) w v))))
-(\lambda (_: T).(\lambda (w0: T).(ty3 g c w w0))) (\lambda (v: T).(\lambda
-(_: T).(ty3 g (CHead c (Bind Abst) w) v u))) (\lambda (v: T).(\lambda (_:
-T).(nf2 (CHead c (Bind Abst) w) v)))) (\lambda (x2: T).(\lambda (x3:
-T).(\lambda (_: (pc3 c (THead (Bind Abst) w x2) x)).(\lambda (H11: (ty3 g c w
-x3)).(\lambda (H12: (ty3 g (CHead c (Bind Abst) w) u x2)).(ex3_2_ind T T
-(\lambda (t2: T).(\lambda (_: T).(pc3 c (THead (Bind Abst) x0 t2) (THead
-(Bind Abst) w u)))) (\lambda (_: T).(\lambda (t0: T).(ty3 g c x0 t0)))
-(\lambda (t2: T).(\lambda (_: T).(ty3 g (CHead c (Bind Abst) x0) x1 t2)))
-(ex4_2 T T (\lambda (v: T).(\lambda (_: T).(eq T (THead (Bind Abst) x0 x1)
-(THead (Bind Abst) w v)))) (\lambda (_: T).(\lambda (w0: T).(ty3 g c w w0)))
-(\lambda (v: T).(\lambda (_: T).(ty3 g (CHead c (Bind Abst) w) v u)))
-(\lambda (v: T).(\lambda (_: T).(nf2 (CHead c (Bind Abst) w) v)))) (\lambda
-(x4: T).(\lambda (x5: T).(\lambda (H13: (pc3 c (THead (Bind Abst) x0 x4)
-(THead (Bind Abst) w u))).(\lambda (_: (ty3 g c x0 x5)).(\lambda (H15: (ty3 g
-(CHead c (Bind Abst) x0) x1 x4)).(land_ind (pc3 c x0 w) (\forall (b:
-B).(\forall (u0: T).(pc3 (CHead c (Bind b) u0) x4 u))) (ex4_2 T T (\lambda
-(v: T).(\lambda (_: T).(eq T (THead (Bind Abst) x0 x1) (THead (Bind Abst) w
-v)))) (\lambda (_: T).(\lambda (w0: T).(ty3 g c w w0))) (\lambda (v:
-T).(\lambda (_: T).(ty3 g (CHead c (Bind Abst) w) v u))) (\lambda (v:
-T).(\lambda (_: T).(nf2 (CHead c (Bind Abst) w) v)))) (\lambda (H16: (pc3 c
-x0 w)).(\lambda (H17: ((\forall (b: B).(\forall (u0: T).(pc3 (CHead c (Bind
-b) u0) x4 u))))).(let H_y \def (pc3_nf2 c x0 w H16 H6 H1) in (let H18 \def
-(eq_ind T x0 (\lambda (t0: T).(ty3 g (CHead c (Bind Abst) t0) x1 x4)) H15 w
-H_y) in (let H19 \def (eq_ind T x0 (\lambda (t0: T).(nf2 (CHead c (Bind Abst)
-t0) x1)) H7 w H_y) in (eq_ind_r T w (\lambda (t0: T).(ex4_2 T T (\lambda (v:
-T).(\lambda (_: T).(eq T (THead (Bind Abst) t0 x1) (THead (Bind Abst) w v))))
-(\lambda (_: T).(\lambda (w0: T).(ty3 g c w w0))) (\lambda (v: T).(\lambda
-(_: T).(ty3 g (CHead c (Bind Abst) w) v u))) (\lambda (v: T).(\lambda (_:
-T).(nf2 (CHead c (Bind Abst) w) v))))) (ex4_2_intro T T (\lambda (v:
-T).(\lambda (_: T).(eq T (THead (Bind Abst) w x1) (THead (Bind Abst) w v))))
-(\lambda (_: T).(\lambda (w0: T).(ty3 g c w w0))) (\lambda (v: T).(\lambda
-(_: T).(ty3 g (CHead c (Bind Abst) w) v u))) (\lambda (v: T).(\lambda (_:
-T).(nf2 (CHead c (Bind Abst) w) v))) x1 x3 (refl_equal T (THead (Bind Abst) w
-x1)) H11 (ty3_conv g (CHead c (Bind Abst) w) u x2 H12 x1 x4 H18 (H17 Abst w))
-H19) x0 H_y)))))) (pc3_gen_abst c x0 w x4 u H13))))))) (ty3_gen_bind g Abst c
-x0 x1 (THead (Bind Abst) w u) H8))))))) (ty3_gen_bind g Abst c w u x H9))))
-(ty3_correct g c (THead (Bind Abst) x0 x1) (THead (Bind Abst) w u) H8)) t
-H5))))))) H4)) (\lambda (H4: (ex nat (\lambda (n: nat).(eq T t (TSort
-n))))).(ex_ind nat (\lambda (n: nat).(eq T t (TSort n))) (ex4_2 T T (\lambda
-(v: T).(\lambda (_: T).(eq T t (THead (Bind Abst) w v)))) (\lambda (_:
-T).(\lambda (w0: T).(ty3 g c w w0))) (\lambda (v: T).(\lambda (_: T).(ty3 g
-(CHead c (Bind Abst) w) v u))) (\lambda (v: T).(\lambda (_: T).(nf2 (CHead c
-(Bind Abst) w) v)))) (\lambda (x: nat).(\lambda (H5: (eq T t (TSort x))).(let
-H6 \def (eq_ind T t (\lambda (t0: T).(ty3 g c t0 (THead (Bind Abst) w u))) H
-(TSort x) H5) in (eq_ind_r T (TSort x) (\lambda (t0: T).(ex4_2 T T (\lambda
-(v: T).(\lambda (_: T).(eq T t0 (THead (Bind Abst) w v)))) (\lambda (_:
-T).(\lambda (w0: T).(ty3 g c w w0))) (\lambda (v: T).(\lambda (_: T).(ty3 g
-(CHead c (Bind Abst) w) v u))) (\lambda (v: T).(\lambda (_: T).(nf2 (CHead c
-(Bind Abst) w) v))))) (pc3_gen_sort_abst c w u (next g x) (ty3_gen_sort g c
-(THead (Bind Abst) w u) x H6) (ex4_2 T T (\lambda (v: T).(\lambda (_: T).(eq
-T (TSort x) (THead (Bind Abst) w v)))) (\lambda (_: T).(\lambda (w0: T).(ty3
-g c w w0))) (\lambda (v: T).(\lambda (_: T).(ty3 g (CHead c (Bind Abst) w) v
-u))) (\lambda (v: T).(\lambda (_: T).(nf2 (CHead c (Bind Abst) w) v))))) t
-H5)))) H4)) (\lambda (H4: (ex3_2 TList nat (\lambda (ws: TList).(\lambda (i:
-nat).(eq T t (THeads (Flat Appl) ws (TLRef i))))) (\lambda (ws:
-TList).(\lambda (_: nat).(nfs2 c ws))) (\lambda (_: TList).(\lambda (i:
-nat).(nf2 c (TLRef i)))))).(ex3_2_ind TList nat (\lambda (ws: TList).(\lambda
-(i: nat).(eq T t (THeads (Flat Appl) ws (TLRef i))))) (\lambda (ws:
-TList).(\lambda (_: nat).(nfs2 c ws))) (\lambda (_: TList).(\lambda (i:
-nat).(nf2 c (TLRef i)))) (ex4_2 T T (\lambda (v: T).(\lambda (_: T).(eq T t
-(THead (Bind Abst) w v)))) (\lambda (_: T).(\lambda (w0: T).(ty3 g c w w0)))
-(\lambda (v: T).(\lambda (_: T).(ty3 g (CHead c (Bind Abst) w) v u)))
-(\lambda (v: T).(\lambda (_: T).(nf2 (CHead c (Bind Abst) w) v)))) (\lambda
-(x0: TList).(\lambda (x1: nat).(\lambda (H5: (eq T t (THeads (Flat Appl) x0
-(TLRef x1)))).(\lambda (_: (nfs2 c x0)).(\lambda (H7: (nf2 c (TLRef
-x1))).(let H8 \def (eq_ind T t (\lambda (t0: T).(ty3 g c t0 (THead (Bind
-Abst) w u))) H (THeads (Flat Appl) x0 (TLRef x1)) H5) in (eq_ind_r T (THeads
-(Flat Appl) x0 (TLRef x1)) (\lambda (t0: T).(ex4_2 T T (\lambda (v:
-T).(\lambda (_: T).(eq T t0 (THead (Bind Abst) w v)))) (\lambda (_:
-T).(\lambda (w0: T).(ty3 g c w w0))) (\lambda (v: T).(\lambda (_: T).(ty3 g
-(CHead c (Bind Abst) w) v u))) (\lambda (v: T).(\lambda (_: T).(nf2 (CHead c
-(Bind Abst) w) v))))) (let H9 \def H2 in ((let H10 \def H8 in (unintro T u
-(\lambda (t0: T).((ty3 g c (THeads (Flat Appl) x0 (TLRef x1)) (THead (Bind
-Abst) w t0)) \to ((ty3_nf2_inv_abst_premise c w t0) \to (ex4_2 T T (\lambda
-(v: T).(\lambda (_: T).(eq T (THeads (Flat Appl) x0 (TLRef x1)) (THead (Bind
-Abst) w v)))) (\lambda (_: T).(\lambda (w0: T).(ty3 g c w w0))) (\lambda (v:
-T).(\lambda (_: T).(ty3 g (CHead c (Bind Abst) w) v t0))) (\lambda (v:
-T).(\lambda (_: T).(nf2 (CHead c (Bind Abst) w) v))))))) (unintro T w
-(\lambda (t0: T).(\forall (x: T).((ty3 g c (THeads (Flat Appl) x0 (TLRef x1))
-(THead (Bind Abst) t0 x)) \to ((ty3_nf2_inv_abst_premise c t0 x) \to (ex4_2 T
-T (\lambda (v: T).(\lambda (_: T).(eq T (THeads (Flat Appl) x0 (TLRef x1))
-(THead (Bind Abst) t0 v)))) (\lambda (_: T).(\lambda (w0: T).(ty3 g c t0
-w0))) (\lambda (v: T).(\lambda (_: T).(ty3 g (CHead c (Bind Abst) t0) v x)))
-(\lambda (v: T).(\lambda (_: T).(nf2 (CHead c (Bind Abst) t0) v))))))))
-(TList_ind (\lambda (t0: TList).(\forall (x: T).(\forall (x2: T).((ty3 g c
-(THeads (Flat Appl) t0 (TLRef x1)) (THead (Bind Abst) x x2)) \to
-((ty3_nf2_inv_abst_premise c x x2) \to (ex4_2 T T (\lambda (v: T).(\lambda
-(_: T).(eq T (THeads (Flat Appl) t0 (TLRef x1)) (THead (Bind Abst) x v))))
-(\lambda (_: T).(\lambda (w0: T).(ty3 g c x w0))) (\lambda (v: T).(\lambda
-(_: T).(ty3 g (CHead c (Bind Abst) x) v x2))) (\lambda (v: T).(\lambda (_:
-T).(nf2 (CHead c (Bind Abst) x) v))))))))) (\lambda (x: T).(\lambda (x2:
-T).(\lambda (H11: (ty3 g c (TLRef x1) (THead (Bind Abst) x x2))).(\lambda
-(H12: (ty3_nf2_inv_abst_premise c x x2)).(or_ind (ex3_3 C T T (\lambda (_:
-C).(\lambda (_: T).(\lambda (t0: T).(pc3 c (lift (S x1) O t0) (THead (Bind
-Abst) x x2))))) (\lambda (e: C).(\lambda (u0: T).(\lambda (_: T).(getl x1 c
-(CHead e (Bind Abbr) u0))))) (\lambda (e: C).(\lambda (u0: T).(\lambda (t0:
-T).(ty3 g e u0 t0))))) (ex3_3 C T T (\lambda (_: C).(\lambda (u0: T).(\lambda
-(_: T).(pc3 c (lift (S x1) O u0) (THead (Bind Abst) x x2))))) (\lambda (e:
-C).(\lambda (u0: T).(\lambda (_: T).(getl x1 c (CHead e (Bind Abst) u0)))))
-(\lambda (e: C).(\lambda (u0: T).(\lambda (t0: T).(ty3 g e u0 t0))))) (ex4_2
-T T (\lambda (v: T).(\lambda (_: T).(eq T (TLRef x1) (THead (Bind Abst) x
-v)))) (\lambda (_: T).(\lambda (w0: T).(ty3 g c x w0))) (\lambda (v:
-T).(\lambda (_: T).(ty3 g (CHead c (Bind Abst) x) v x2))) (\lambda (v:
-T).(\lambda (_: T).(nf2 (CHead c (Bind Abst) x) v)))) (\lambda (H13: (ex3_3 C
-T T (\lambda (_: C).(\lambda (_: T).(\lambda (t0: T).(pc3 c (lift (S x1) O
-t0) (THead (Bind Abst) x x2))))) (\lambda (e: C).(\lambda (u0: T).(\lambda
-(_: T).(getl x1 c (CHead e (Bind Abbr) u0))))) (\lambda (e: C).(\lambda (u0:
-T).(\lambda (t0: T).(ty3 g e u0 t0)))))).(ex3_3_ind C T T (\lambda (_:
-C).(\lambda (_: T).(\lambda (t0: T).(pc3 c (lift (S x1) O t0) (THead (Bind
-Abst) x x2))))) (\lambda (e: C).(\lambda (u0: T).(\lambda (_: T).(getl x1 c
-(CHead e (Bind Abbr) u0))))) (\lambda (e: C).(\lambda (u0: T).(\lambda (t0:
-T).(ty3 g e u0 t0)))) (ex4_2 T T (\lambda (v: T).(\lambda (_: T).(eq T (TLRef
-x1) (THead (Bind Abst) x v)))) (\lambda (_: T).(\lambda (w0: T).(ty3 g c x
-w0))) (\lambda (v: T).(\lambda (_: T).(ty3 g (CHead c (Bind Abst) x) v x2)))
-(\lambda (v: T).(\lambda (_: T).(nf2 (CHead c (Bind Abst) x) v)))) (\lambda
-(x3: C).(\lambda (x4: T).(\lambda (x5: T).(\lambda (_: (pc3 c (lift (S x1) O
-x5) (THead (Bind Abst) x x2))).(\lambda (H15: (getl x1 c (CHead x3 (Bind
-Abbr) x4))).(\lambda (_: (ty3 g x3 x4 x5)).(nf2_gen_lref c x3 x4 x1 H15 H7
-(ex4_2 T T (\lambda (v: T).(\lambda (_: T).(eq T (TLRef x1) (THead (Bind
-Abst) x v)))) (\lambda (_: T).(\lambda (w0: T).(ty3 g c x w0))) (\lambda (v:
-T).(\lambda (_: T).(ty3 g (CHead c (Bind Abst) x) v x2))) (\lambda (v:
-T).(\lambda (_: T).(nf2 (CHead c (Bind Abst) x) v))))))))))) H13)) (\lambda
-(H13: (ex3_3 C T T (\lambda (_: C).(\lambda (u0: T).(\lambda (_: T).(pc3 c
-(lift (S x1) O u0) (THead (Bind Abst) x x2))))) (\lambda (e: C).(\lambda (u0:
-T).(\lambda (_: T).(getl x1 c (CHead e (Bind Abst) u0))))) (\lambda (e:
-C).(\lambda (u0: T).(\lambda (t0: T).(ty3 g e u0 t0)))))).(ex3_3_ind C T T
-(\lambda (_: C).(\lambda (u0: T).(\lambda (_: T).(pc3 c (lift (S x1) O u0)
-(THead (Bind Abst) x x2))))) (\lambda (e: C).(\lambda (u0: T).(\lambda (_:
-T).(getl x1 c (CHead e (Bind Abst) u0))))) (\lambda (e: C).(\lambda (u0:
-T).(\lambda (t0: T).(ty3 g e u0 t0)))) (ex4_2 T T (\lambda (v: T).(\lambda
-(_: T).(eq T (TLRef x1) (THead (Bind Abst) x v)))) (\lambda (_: T).(\lambda
-(w0: T).(ty3 g c x w0))) (\lambda (v: T).(\lambda (_: T).(ty3 g (CHead c
-(Bind Abst) x) v x2))) (\lambda (v: T).(\lambda (_: T).(nf2 (CHead c (Bind
-Abst) x) v)))) (\lambda (x3: C).(\lambda (x4: T).(\lambda (x5: T).(\lambda
-(H14: (pc3 c (lift (S x1) O x4) (THead (Bind Abst) x x2))).(\lambda (H15:
-(getl x1 c (CHead x3 (Bind Abst) x4))).(\lambda (_: (ty3 g x3 x4 x5)).(let
-H_x0 \def (H12 x3 x4 x1 H15 TNil H14) in (let H17 \def H_x0 in (False_ind
-(ex4_2 T T (\lambda (v: T).(\lambda (_: T).(eq T (TLRef x1) (THead (Bind
-Abst) x v)))) (\lambda (_: T).(\lambda (w0: T).(ty3 g c x w0))) (\lambda (v:
-T).(\lambda (_: T).(ty3 g (CHead c (Bind Abst) x) v x2))) (\lambda (v:
-T).(\lambda (_: T).(nf2 (CHead c (Bind Abst) x) v)))) H17))))))))) H13))
-(ty3_gen_lref g c (THead (Bind Abst) x x2) x1 H11)))))) (\lambda (t0:
-T).(\lambda (t1: TList).(\lambda (H11: ((\forall (x: T).(\forall (x2:
-T).((ty3 g c (THeads (Flat Appl) t1 (TLRef x1)) (THead (Bind Abst) x x2)) \to
-((ty3_nf2_inv_abst_premise c x x2) \to (ex4_2 T T (\lambda (v: T).(\lambda
-(_: T).(eq T (THeads (Flat Appl) t1 (TLRef x1)) (THead (Bind Abst) x v))))
-(\lambda (_: T).(\lambda (w0: T).(ty3 g c x w0))) (\lambda (v: T).(\lambda
-(_: T).(ty3 g (CHead c (Bind Abst) x) v x2))) (\lambda (v: T).(\lambda (_:
-T).(nf2 (CHead c (Bind Abst) x) v)))))))))).(\lambda (x: T).(\lambda (x2:
-T).(\lambda (H12: (ty3 g c (THead (Flat Appl) t0 (THeads (Flat Appl) t1
-(TLRef x1))) (THead (Bind Abst) x x2))).(\lambda (H13:
-(ty3_nf2_inv_abst_premise c x x2)).(ex3_2_ind T T (\lambda (u0: T).(\lambda
-(t2: T).(pc3 c (THead (Flat Appl) t0 (THead (Bind Abst) u0 t2)) (THead (Bind
-Abst) x x2)))) (\lambda (u0: T).(\lambda (t2: T).(ty3 g c (THeads (Flat Appl)
-t1 (TLRef x1)) (THead (Bind Abst) u0 t2)))) (\lambda (u0: T).(\lambda (_:
-T).(ty3 g c t0 u0))) (ex4_2 T T (\lambda (v: T).(\lambda (_: T).(eq T (THead
-(Flat Appl) t0 (THeads (Flat Appl) t1 (TLRef x1))) (THead (Bind Abst) x v))))
-(\lambda (_: T).(\lambda (w0: T).(ty3 g c x w0))) (\lambda (v: T).(\lambda
-(_: T).(ty3 g (CHead c (Bind Abst) x) v x2))) (\lambda (v: T).(\lambda (_:
-T).(nf2 (CHead c (Bind Abst) x) v)))) (\lambda (x3: T).(\lambda (x4:
-T).(\lambda (H14: (pc3 c (THead (Flat Appl) t0 (THead (Bind Abst) x3 x4))
-(THead (Bind Abst) x x2))).(\lambda (H15: (ty3 g c (THeads (Flat Appl) t1
-(TLRef x1)) (THead (Bind Abst) x3 x4))).(\lambda (_: (ty3 g c t0 x3)).(let
-H_y \def (ty3_nf2_gen__ty3_nf2_inv_abst_aux c x x2 H13 t0 x3 x4 H14) in (let
-H_x0 \def (H11 x3 x4 H15 H_y) in (let H17 \def H_x0 in (ex4_2_ind T T
-(\lambda (v: T).(\lambda (_: T).(eq T (THeads (Flat Appl) t1 (TLRef x1))
-(THead (Bind Abst) x3 v)))) (\lambda (_: T).(\lambda (w0: T).(ty3 g c x3
-w0))) (\lambda (v: T).(\lambda (_: T).(ty3 g (CHead c (Bind Abst) x3) v x4)))
-(\lambda (v: T).(\lambda (_: T).(nf2 (CHead c (Bind Abst) x3) v))) (ex4_2 T T
-(\lambda (v: T).(\lambda (_: T).(eq T (THead (Flat Appl) t0 (THeads (Flat
-Appl) t1 (TLRef x1))) (THead (Bind Abst) x v)))) (\lambda (_: T).(\lambda
-(w0: T).(ty3 g c x w0))) (\lambda (v: T).(\lambda (_: T).(ty3 g (CHead c
-(Bind Abst) x) v x2))) (\lambda (v: T).(\lambda (_: T).(nf2 (CHead c (Bind
-Abst) x) v)))) (\lambda (x5: T).(\lambda (x6: T).(\lambda (H18: (eq T (THeads
-(Flat Appl) t1 (TLRef x1)) (THead (Bind Abst) x3 x5))).(\lambda (_: (ty3 g c
-x3 x6)).(\lambda (_: (ty3 g (CHead c (Bind Abst) x3) x5 x4)).(\lambda (_:
-(nf2 (CHead c (Bind Abst) x3) x5)).(TList_ind (\lambda (t2: TList).((eq T
-(THeads (Flat Appl) t2 (TLRef x1)) (THead (Bind Abst) x3 x5)) \to (ex4_2 T T
-(\lambda (v: T).(\lambda (_: T).(eq T (THead (Flat Appl) t0 (THeads (Flat
-Appl) t2 (TLRef x1))) (THead (Bind Abst) x v)))) (\lambda (_: T).(\lambda
-(w0: T).(ty3 g c x w0))) (\lambda (v: T).(\lambda (_: T).(ty3 g (CHead c
-(Bind Abst) x) v x2))) (\lambda (v: T).(\lambda (_: T).(nf2 (CHead c (Bind
-Abst) x) v)))))) (\lambda (H22: (eq T (THeads (Flat Appl) TNil (TLRef x1))
-(THead (Bind Abst) x3 x5))).(let H23 \def (eq_ind T (TLRef x1) (\lambda (ee:
-T).(match ee in T return (\lambda (_: T).Prop) with [(TSort _) \Rightarrow
-False | (TLRef _) \Rightarrow True | (THead _ _ _) \Rightarrow False])) I
-(THead (Bind Abst) x3 x5) H22) in (False_ind (ex4_2 T T (\lambda (v:
-T).(\lambda (_: T).(eq T (THead (Flat Appl) t0 (THeads (Flat Appl) TNil
-(TLRef x1))) (THead (Bind Abst) x v)))) (\lambda (_: T).(\lambda (w0: T).(ty3
-g c x w0))) (\lambda (v: T).(\lambda (_: T).(ty3 g (CHead c (Bind Abst) x) v
-x2))) (\lambda (v: T).(\lambda (_: T).(nf2 (CHead c (Bind Abst) x) v))))
-H23))) (\lambda (t2: T).(\lambda (t3: TList).(\lambda (_: (((eq T (THeads
-(Flat Appl) t3 (TLRef x1)) (THead (Bind Abst) x3 x5)) \to (ex4_2 T T (\lambda
-(v: T).(\lambda (_: T).(eq T (THead (Flat Appl) t0 (THeads (Flat Appl) t3
-(TLRef x1))) (THead (Bind Abst) x v)))) (\lambda (_: T).(\lambda (w0: T).(ty3
-g c x w0))) (\lambda (v: T).(\lambda (_: T).(ty3 g (CHead c (Bind Abst) x) v
-x2))) (\lambda (v: T).(\lambda (_: T).(nf2 (CHead c (Bind Abst) x)
-v))))))).(\lambda (H22: (eq T (THeads (Flat Appl) (TCons t2 t3) (TLRef x1))
-(THead (Bind Abst) x3 x5))).(let H23 \def (eq_ind T (THead (Flat Appl) t2
-(THeads (Flat Appl) t3 (TLRef x1))) (\lambda (ee: T).(match ee in T return
-(\lambda (_: T).Prop) with [(TSort _) \Rightarrow False | (TLRef _)
-\Rightarrow False | (THead k _ _) \Rightarrow (match k in K return (\lambda
-(_: K).Prop) with [(Bind _) \Rightarrow False | (Flat _) \Rightarrow
-True])])) I (THead (Bind Abst) x3 x5) H22) in (False_ind (ex4_2 T T (\lambda
-(v: T).(\lambda (_: T).(eq T (THead (Flat Appl) t0 (THeads (Flat Appl) (TCons
-t2 t3) (TLRef x1))) (THead (Bind Abst) x v)))) (\lambda (_: T).(\lambda (w0:
-T).(ty3 g c x w0))) (\lambda (v: T).(\lambda (_: T).(ty3 g (CHead c (Bind
-Abst) x) v x2))) (\lambda (v: T).(\lambda (_: T).(nf2 (CHead c (Bind Abst) x)
-v)))) H23)))))) t1 H18))))))) H17))))))))) (ty3_gen_appl g c t0 (THeads (Flat
-Appl) t1 (TLRef x1)) (THead (Bind Abst) x x2) H12))))))))) x0)) H10)) H9)) t
-H5))))))) H4)) H3))))))))))).
-(* COMMENTS
-Initial nodes: 5333
-END *)
-
projects / helm.git / blobdiff