lemma cpes_cprs_trans (h) (n) (G) (L) (T0):
∀T1. ❪G,L❫ ⊢ T1 ⬌*[h,n,0] T0 →
- ∀T2. ❪G,L❫ ⊢ T0 ➡*[h] T2 → ❪G,L❫ ⊢ T1 ⬌*[h,n,0] T2.
+ ∀T2. ❪G,L❫ ⊢ T0 ➡*[h,0] T2 → ❪G,L❫ ⊢ T1 ⬌*[h,n,0] T2.
#h #n #G #L #T0 #T1 * #T #HT1 #HT0 #T2 #HT02
elim (cprs_conf … HT0 … HT02) -T0 #T0 #HT0 #HT20
/3 width=3 by cpms_div, cpms_cprs_trans/
lemma cpes_cpms_div (h) (n) (n1) (n2) (G) (L) (T0):
∀T1. ❪G,L❫ ⊢ T1 ⬌*[h,n,n1] T0 →
- ∀T2. ❪G,L❫ ⊢ T2 ➡*[n2,h] T0 → ❪G,L❫ ⊢ T1 ⬌*[h,n,n2+n1] T2.
+ ∀T2. ❪G,L❫ ⊢ T2 ➡*[h,n2] T0 → ❪G,L❫ ⊢ T1 ⬌*[h,n,n2+n1] T2.
#h #n #n1 #n2 #G #L #T0 #T1 * #T #HT1 #HT0 #T2 #HT20
lapply (cpms_trans … HT20 … HT0) -T0 #HT2
/2 width=3 by cpms_div/