(**************************************************************************)
include "delayed_updating/unwind/unwind2_prototerm_eq.ma".
-include "delayed_updating/unwind/unwind2_path_structure.ma".
+include "delayed_updating/unwind/unwind2_path_append.ma".
include "delayed_updating/substitution/fsubst.ma".
include "delayed_updating/syntax/preterm.ma".
include "delayed_updating/syntax/prototerm_proper.ma".
-(* UNWIND FOR PRETERM *******************************************************)
+(* TAILED UNWIND FOR PRETERM ************************************************)
(* Constructions with fsubst ************************************************)
lemma unwind2_term_fsubst_sn (f) (t) (u) (p): u Ļµ š ā
- (ā¼[f]t)[ā(āp)āā¼[ā¶[f]pį“æ]u] ā ā¼[f](t[āpāu]).
+ (ā¼[f]t)[ā(āp)āā¼[ā¶[f]p]u] ā ā¼[f](t[āpāu]).
#f #t #u #p #Hu #ql * *
[ #rl * #r #Hr #H1 #H2 destruct
>unwind2_path_append_proper_dx
/4 width=5 by in_comp_unwind2_path_term, in_comp_tpc_trans, or_introl, ex2_intro/
| * #q #Hq #H1 #H0
@(ex2_intro ā¦ H1) @or_intror @conj // *
- [ <list_append_empty_dx #H2 destruct
+ [ <list_append_empty_sn #H2 destruct
elim (unwind2_path_root f q) #r #_ #Hr /2 width=2 by/
| #l #r #H2 destruct
- @H0 -H0 [| <unwind2_path_append_proper_dx /2 width=3 by ppc_lcons/ ]
+ @H0 -H0 [| <unwind2_path_append_proper_dx /2 width=3 by ppc_rcons/ ]
]
]
qed-.
lemma unwind2_term_fsubst_dx (f) (t) (u) (p): u Ļµ š ā p Ļµ āµt ā t Ļµ š ā
- ā¼[f](t[āpāu]) ā (ā¼[f]t)[ā(āp)āā¼[ā¶[f]pį“æ]u].
+ ā¼[f](t[āpāu]) ā (ā¼[f]t)[ā(āp)āā¼[ā¶[f]p]u].
#f #t #u #p #Hu #H1p #H2p #ql * #q * *
[ #r #Hu #H1 #H2 destruct
@or_introl @ex2_intro
/2 width=3 by ex2_intro/
| #Hq #H0 #H1 destruct
@or_intror @conj [ /2 width=1 by in_comp_unwind2_path_term/ ] *
- [ <list_append_empty_dx #Hr @(H0 ā¦ (š)) -H0
- <list_append_empty_dx @H2p -H2p
- /2 width=2 by unwind_gen_des_structure, prototerm_in_comp_root/
+ [ <list_append_empty_sn #Hr @(H0 ā¦ (š)) -H0
+ <list_append_empty_sn @H2p -H2p
+ /2 width=2 by unwind2_path_des_structure, prototerm_in_comp_root/
| #l #r #Hr
elim (unwind2_path_inv_append_proper_dx ā¦ Hr) -Hr // #s1 #s2 #Hs1 #_ #H1 destruct
lapply (H2p ā¦ Hs1) -H2p -Hs1 /2 width=2 by ex_intro/
qed-.
lemma unwind2_term_fsubst (f) (t) (u) (p): u Ļµ š ā p Ļµ āµt ā t Ļµ š ā
- (ā¼[f]t)[ā(āp)āā¼[ā¶[f]pį“æ]u] ā ā¼[f](t[āpāu]).
+ (ā¼[f]t)[ā(āp)āā¼[ā¶[f]p]u] ā ā¼[f](t[āpāu]).
/4 width=3 by unwind2_term_fsubst_sn, conj, unwind2_term_fsubst_dx/ qed.