(* Basic_2A1: uses: scpes_refl *)
lemma cpes_refl_aaa (h) (n):
- â\88\80G,L,T,A. â¦\83G,Lâ¦\84 â\8a¢ T â\81\9d A â\86\92 â¦\83G,Lâ¦\84 ⊢ T ⬌*[h,n,n] T.
+ â\88\80G,L,T,A. â\9dªG,Lâ\9d« â\8a¢ T â\81\9d A â\86\92 â\9dªG,Lâ\9d« ⊢ T ⬌*[h,n,n] T.
#h #n #G #L #T #A #HA
elim (cpms_total_aaa h … n … HA) #U #HTU
/2 width=3 by cpms_div/
(* Basic_2A1: uses: scpes_aaa_mono *)
theorem cpes_aaa_mono (h) (n1) (n2):
- â\88\80G,L,T1,T2. â¦\83G,Lâ¦\84 ⊢ T1 ⬌*[h,n1,n2] T2 →
- â\88\80A1. â¦\83G,Lâ¦\84 â\8a¢ T1 â\81\9d A1 â\86\92 â\88\80A2. â¦\83G,Lâ¦\84 ⊢ T2 ⁝ A2 → A1 = A2.
+ â\88\80G,L,T1,T2. â\9dªG,Lâ\9d« ⊢ T1 ⬌*[h,n1,n2] T2 →
+ â\88\80A1. â\9dªG,Lâ\9d« â\8a¢ T1 â\81\9d A1 â\86\92 â\88\80A2. â\9dªG,Lâ\9d« ⊢ T2 ⁝ A2 → A1 = A2.
#h #n1 #n2 #G #L #T1 #T2 * #T #HT1 #HT2 #A1 #HA1 #A2 #HA2
lapply (cpms_aaa_conf … HA1 … HT1) -T1 #HA1
lapply (cpms_aaa_conf … HA2 … HT2) -T2 #HA2