(* Advanced forward lemmas **************************************************)
lemma cpes_fwd_abst_bi (h) (n1) (n2) (p1) (p2) (G) (L):
- â\88\80W1,W2,T1,T2. â¦\83G,Lâ¦\84 â\8a¢ â\93\9b{p1}W1.T1 â¬\8c*[h,n1,n2] â\93\9b{p2}W2.T2 →
- â\88§â\88§ p1 = p2 & â¦\83G,Lâ¦\84 ⊢ W1 ⬌*[h,0,O] W2.
+ â\88\80W1,W2,T1,T2. â\9d¨G,Lâ\9d© â\8a¢ â\93\9b[p1]W1.T1 â¬\8c*[h,n1,n2] â\93\9b[p2]W2.T2 →
+ â\88§â\88§ p1 = p2 & â\9d¨G,Lâ\9d© ⊢ W1 ⬌*[h,0,O] W2.
#h #n1 #n2 #p1 #p2 #G #L #W1 #W2 #T1 #T2 * #X #H1 #H2
elim (cpms_inv_abst_sn … H1) #W0 #X0 #HW10 #_ #H destruct
elim (cpms_inv_abst_bi … H2) #H #HW20 #_ destruct
(* Main properties **********************************************************)
theorem cpes_cpes_trans (h) (n1) (n2) (G) (L) (T):
- â\88\80T1. â¦\83G,Lâ¦\84 ⊢ T ⬌*[h,n1,0] T1 →
- â\88\80T2. â¦\83G,Lâ¦\84 â\8a¢ T1 â¬\8c*[h,0,n2] T2 â\86\92 â¦\83G,Lâ¦\84 ⊢ T ⬌*[h,n1,n2] T2.
+ â\88\80T1. â\9d¨G,Lâ\9d© ⊢ T ⬌*[h,n1,0] T1 →
+ â\88\80T2. â\9d¨G,Lâ\9d© â\8a¢ T1 â¬\8c*[h,0,n2] T2 â\86\92 â\9d¨G,Lâ\9d© ⊢ T ⬌*[h,n1,n2] T2.
#h #n1 #n2 #G #L #T #T1 #HT1 #T2 * #X #HX1 #HX2
lapply (cpes_cprs_trans … HT1 … HX1) -T1 #HTX
lapply (cpes_cpms_div … HTX … HX2) -X //