/3 width=5 by cpms_fwd_cpxs, cpxs_aaa_conf/ qed-.
lemma cpms_total_aaa (h) (G) (L) (n) (A):
- â\88\80T. â\9dªG,Lâ\9d« â\8a¢ T â\81\9d A â\86\92 â\88\83U. â\9dªG,Lâ\9d« ⊢ T ➡*[h,n] U.
+ â\88\80T. â\9d¨G,Lâ\9d© â\8a¢ T â\81\9d A â\86\92 â\88\83U. â\9d¨G,Lâ\9d© ⊢ T ➡*[h,n] U.
#h #G #L #n elim n -n
[ /2 width=3 by ex_intro/
| #n #IH #A #T1 #HT1 <plus_SO_dx
qed-.
lemma cpms_abst_dx_le_aaa (h) (G) (L) (T) (W) (p):
- â\88\80A. â\9dªG,Lâ\9d« ⊢ T ⁝ A →
- â\88\80n1,U1. â\9dªG,Lâ\9d« ⊢ T ➡*[h,n1] ⓛ[p]W.U1 → ∀n2. n1 ≤ n2 →
- â\88\83â\88\83U2. â\9dªG,Lâ\9d« â\8a¢ T â\9e¡*[h,n2] â\93\9b[p]W.U2 & â\9dªG,L.â\93\9bWâ\9d« ⊢ U1 ➡*[h,n2-n1] U2.
+ â\88\80A. â\9d¨G,Lâ\9d© ⊢ T ⁝ A →
+ â\88\80n1,U1. â\9d¨G,Lâ\9d© ⊢ T ➡*[h,n1] ⓛ[p]W.U1 → ∀n2. n1 ≤ n2 →
+ â\88\83â\88\83U2. â\9d¨G,Lâ\9d© â\8a¢ T â\9e¡*[h,n2] â\93\9b[p]W.U2 & â\9d¨G,L.â\93\9bWâ\9d© ⊢ U1 ➡*[h,n2-n1] U2.
#h #G #L #T #W #p #A #HA #n1 #U1 #HTU1 #n2 #Hn12
lapply (cpms_aaa_conf … HA … HTU1) -HA #HA
elim (cpms_total_aaa h … (n2-n1) … HA) -HA #X #H