(* Forward lemmas with t-bound rt-computation for terms *********************)
lemma cpts_fwd_cpms (h) (n) (G) (L):
- ∀T1,T2. ❪G,L❫ ⊢ T1 ⬆*[h,n] T2 → ❪G,L❫ ⊢ T1 ➡*[n,h] T2.
+ ∀T1,T2. ❪G,L❫ ⊢ T1 ⬆*[h,n] T2 → ❪G,L❫ ⊢ T1 ➡*[h,n] T2.
#h #n #G #L #T1 #T2 #H
@(cpts_ind_dx … H) -n -T2 [ // ]
#n1 #n2 #T #T2 #_ #IH #HT2
lemma cpts_cprs_trans (h) (n) (G) (L) (T):
∀T1. ❪G,L❫ ⊢ T1 ⬆*[h,n] T →
- ∀T2. ❪G,L❫ ⊢ T ➡*[h] T2 → ❪G,L❫ ⊢ T1 ➡*[n,h] T2.
+ ∀T2. ❪G,L❫ ⊢ T ➡*[h,0] T2 → ❪G,L❫ ⊢ T1 ➡*[h,n] T2.
#h #n #G #L #T #T1 #HT1 #T2 #HT2
/3 width=3 by cpts_fwd_cpms, cpms_cprs_trans/ qed-.