(* Properties with append for local environments ****************************)
-lemma frees_append_void: â\88\80f,K,T. K â\8a¢ ð\9d\90\85+â¦\83Tâ¦\84 â\89\98 f â\86\92 â\93§.K â\8a¢ ð\9d\90\85+â¦\83Tâ¦\84 ≘ f.
+lemma frees_append_void: â\88\80f,K,T. K â\8a¢ ð\9d\90\85+â\9dªTâ\9d« â\89\98 f â\86\92 â\93§.K â\8a¢ ð\9d\90\85+â\9dªTâ\9d« ≘ f.
#f #K #T #H elim H -f -K -T
[ /2 width=1 by frees_sort/
| #f * /3 width=1 by frees_atom, frees_unit, frees_lref/
(* Inversion lemmas with append for local environments **********************)
fact frees_inv_append_void_aux:
- â\88\80f,L,T. L â\8a¢ ð\9d\90\85+â¦\83Tâ¦\84 ≘ f →
- â\88\80K. L = â\93§.K â\86\92 K â\8a¢ ð\9d\90\85+â¦\83Tâ¦\84 ≘ f.
+ â\88\80f,L,T. L â\8a¢ ð\9d\90\85+â\9dªTâ\9d« ≘ f →
+ â\88\80K. L = â\93§.K â\86\92 K â\8a¢ ð\9d\90\85+â\9dªTâ\9d« ≘ f.
#f #L #T #H elim H -f -L -T
[ /2 width=1 by frees_sort/
| #f #i #_ #K #H
]
qed-.
-lemma frees_inv_append_void: â\88\80f,K,T. â\93§.K â\8a¢ ð\9d\90\85+â¦\83Tâ¦\84 â\89\98 f â\86\92 K â\8a¢ ð\9d\90\85+â¦\83Tâ¦\84 ≘ f.
+lemma frees_inv_append_void: â\88\80f,K,T. â\93§.K â\8a¢ ð\9d\90\85+â\9dªTâ\9d« â\89\98 f â\86\92 K â\8a¢ ð\9d\90\85+â\9dªTâ\9d« ≘ f.
/2 width=3 by frees_inv_append_void_aux/ qed-.