(* Properties with preorder for applicability domains ***********************)
lemma cnv_acle_trans (h) (a1) (a2):
- a1 â\8a\86 a2 â\86\92 â\88\80G,L,T. â¦\83G,Lâ¦\84 â\8a¢ T ![h,a1] â\86\92 â¦\83G,Lâ¦\84 ⊢ T ![h,a2].
+ a1 â\8a\86 a2 â\86\92 â\88\80G,L,T. â\9dªG,Lâ\9d« â\8a¢ T ![h,a1] â\86\92 â\9dªG,Lâ\9d« ⊢ T ![h,a2].
#h #a1 #a2 #Ha12 #G #L #T #H elim H -G -L -T
[ /1 width=1 by cnv_sort/
| /3 width=1 by cnv_zero/
qed-.
lemma cnv_acle_omega (h) (a):
- â\88\80G,L,T. â¦\83G,Lâ¦\84 â\8a¢ T ![h,a] â\86\92 â¦\83G,Lâ¦\84 ⊢ T ![h,𝛚].
+ â\88\80G,L,T. â\9dªG,Lâ\9d« â\8a¢ T ![h,a] â\86\92 â\9dªG,Lâ\9d« ⊢ T ![h,𝛚].
/3 width=3 by cnv_acle_trans, acle_omega/ qed-.
lemma cnv_acle_one (h) (a) (n):
- â\88\80G,L,T. â¦\83G,Lâ¦\84 â\8a¢ T ![h,ð\9d\9f\8f] â\86\92 ad a n â\86\92 â¦\83G,Lâ¦\84 ⊢ T ![h,a].
+ â\88\80G,L,T. â\9dªG,Lâ\9d« â\8a¢ T ![h,ð\9d\9f\8f] â\86\92 ad a n â\86\92 â\9dªG,Lâ\9d« ⊢ T ![h,a].
/3 width=3 by cnv_acle_trans, acle_one/ qed-.