3 (* NOTE: This can be generalized removing the last premise *)
4 Lemma ty3_gen_cvoid: (g:?; c:?; t1,t2:?) (ty3 g c t1 t2) ->
5 (e:?; u:?; d:?) (getl d c (CHead e (Bind Void) u)) ->
6 (a:?) (drop (1) d c a) ->
7 (EX y1 y2 | t1 = (lift (1) d y1) &
12 Lemma ty3_gen_appl_nf2: (g:?; c:?; w,v,x:?) (ty3 g c (THead (Flat Appl) w v) x) ->
13 (EX u t | (pc3 c (THead (Flat Appl) w (THead (Bind Abst) u t)) x) &
14 (ty3 g c v (THead (Bind Abst) u t)) &
16 (nf2 c (THead (Bind Abst) u t))
19 Lemma ty3_arity: (g:?; c:?; t1,t2:?) (ty3 g c t1 t2) ->
20 (EX a1 | (arity g c t1 a1) &
21 (arity g c t2 (asucc g a1))
24 Lemma ty3_acyclic: (g:?; c:?; t,u:?)
25 (ty3 g c t u) -> (pc3 c u t) -> (P:Prop) P.
27 Theorem pc3_abst_dec: (g:?; c:?; u1,t1:?) (ty3 g c u1 t1) ->
28 (u2,t2:?) (ty3 g c u2 t2) ->
29 (EX u v2 | (pc3 c u1 (THead (Bind Abst) u2 u)) &
30 (ty3 g c (THead (Bind Abst) v2 u) t1) &
31 (pr3 c u2 v2) & (nf2 c v2)
33 ((u:?) (pc3 c u1 (THead (Bind Abst) u2 u)) -> False).