(* Forward lemmas with t-bound rt-computation for terms *********************)
lemma cpts_fwd_cpms (h) (n) (G) (L):
- â\88\80T1,T2. â¦\83G,Lâ¦\84 â\8a¢ T1 â¬\86*[h,n] T2 â\86\92 â¦\83G,Lâ¦\84 ⊢ T1 ➡*[n,h] T2.
+ â\88\80T1,T2. â\9dªG,Lâ\9d« â\8a¢ T1 â¬\86*[h,n] T2 â\86\92 â\9dªG,Lâ\9d« ⊢ T1 ➡*[n,h] T2.
#h #n #G #L #T1 #T2 #H
@(cpts_ind_dx … H) -n -T2 [ // ]
#n1 #n2 #T #T2 #_ #IH #HT2
qed-.
lemma cpts_cprs_trans (h) (n) (G) (L) (T):
- â\88\80T1. â¦\83G,Lâ¦\84 ⊢ T1 ⬆*[h,n] T →
- â\88\80T2. â¦\83G,Lâ¦\84 â\8a¢ T â\9e¡*[h] T2 â\86\92 â¦\83G,Lâ¦\84 ⊢ T1 ➡*[n,h] T2.
+ â\88\80T1. â\9dªG,Lâ\9d« ⊢ T1 ⬆*[h,n] T →
+ â\88\80T2. â\9dªG,Lâ\9d« â\8a¢ T â\9e¡*[h] T2 â\86\92 â\9dªG,Lâ\9d« ⊢ T1 ➡*[n,h] T2.
#h #n #G #L #T #T1 #HT1 #T2 #HT2
/3 width=3 by cpts_fwd_cpms, cpms_cprs_trans/ qed-.