+++ /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 *)
-(* *)
-(**************************************************************************)
-
-include "delayed_updating/unwind1/unwind_prototerm_eq.ma".
-include "delayed_updating/unwind1/unwind_structure.ma".
-include "delayed_updating/substitution/fsubst.ma".
-include "delayed_updating/syntax/preterm.ma".
-include "delayed_updating/syntax/prototerm_proper.ma".
-
-(* UNWIND FOR PROTOTERM *****************************************************)
-
-(* Constructions with fsubst ************************************************)
-
-lemma unwind_fsubst_sn (f) (t) (u) (p): u Ļµ š ā
- (ā¼[f]t)[ā(āp)āā¼[ā¼[p]f]u] ā ā¼[f](t[āpāu]).
-#f #t #u #p #Hu #ql * *
-[ #rl * #r #Hr #H1 #H2 destruct
- >unwind_append_proper_dx
- /4 width=5 by in_comp_unwind_bi, in_ppc_comp_trans, or_introl, ex2_intro/
-| * #q #Hq #H1 #H0
- @(ex2_intro ā¦ H1) @or_intror @conj // *
- [ <list_append_empty_dx #H2 destruct
- elim (unwind_path_root f q) #r #_ #Hr /2 width=2 by/
- | #l #r #H2 destruct
- @H0 -H0 [| <unwind_append_proper_dx /2 width=3 by ppc_lcons/ ]
- ]
-]
-qed-.
-
-lemma unwind_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[ā¼[p]f]u].
-#f #t #u #p #Hu #H1p #H2p #ql * #q * *
-[ #r #Hu #H1 #H2 destruct
- @or_introl @ex2_intro
- [|| <unwind_append_proper_dx /2 width=5 by in_ppc_comp_trans/ ]
- /2 width=3 by ex2_intro/
-| #Hq #H0 #H1 destruct
- @or_intror @conj [ /2 width=1 by in_comp_unwind_bi/ ] *
- [ <list_append_empty_dx #Hr @(H0 ā¦ (š)) -H0
- <list_append_empty_dx @H2p -H2p /2 width=1 by prototerm_in_comp_root/
- | #l #r #Hr
- elim (unwind_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 unwind_fsubst (f) (t) (u) (p): u Ļµ š ā p Ļµ āµt ā t Ļµ š ā
- (ā¼[f]t)[ā(āp)āā¼[ā¼[p]f]u] ā ā¼[f](t[āpāu]).
-/4 width=3 by unwind_fsubst_sn, conj, unwind_fsubst_dx/ qed.