(∀L1,T1. h ⊢ ⦃L0, T0⦄ >[g] ⦃L1, T1⦄ → IH_ssta_ltpr_tpr h g L1 T1) →
(∀L1,T1. h ⊢ ⦃L0, T0⦄ >[g] ⦃L1, T1⦄ → IH_snv_ssta h g L1 T1) →
(∀L1,T1. h ⊢ ⦃L0, T0⦄ >[g] ⦃L1, T1⦄ → IH_snv_lsubsv h g L1 T1) →
- â\88\80L2,T. h â\8a¢ â¦\83L0, T0â¦\84 >[g] â¦\83L2, Tâ¦\84 â\86\92 â¦\83h, L2â¦\84 â\8a© T :[g] →
- ∀L1. h ⊢ L1 ⊩:⊑[g] L2 → ∀U2. ⦃h, L2⦄ ⊢ T •*[g] U2 →
+ â\88\80L2,T. h â\8a¢ â¦\83L0, T0â¦\84 >[g] â¦\83L2, Tâ¦\84 â\86\92 â¦\83h, L2â¦\84 â\8a¢ T ¡[g] →
+ ∀L1. h ⊢ L1 ¡⊑[g] L2 → ∀U2. ⦃h, L2⦄ ⊢ T •*[g] U2 →
∃∃U1. ⦃h, L1⦄ ⊢ T •*[g] U1 & L1 ⊢ U1 ⬌* U2.
#h #g #L0 #T0 #IH4 #IH3 #IH2 #IH1 #L2 #T #HLT0 #HT #L1 #HL12 #U2 #H @(sstas_ind … H) -U2 [ /2 width=3/ ]
#U2 #W #l #HTU2 #HU2W * #U1 #HTU1 #HU12
(∀L1,T1. h ⊢ ⦃L0, T0⦄ >[g] ⦃L1, T1⦄ → IH_ssta_ltpr_tpr h g L1 T1) →
(∀L1,T1. h ⊢ ⦃L0, T0⦄ >[g] ⦃L1, T1⦄ → IH_snv_ssta h g L1 T1) →
(∀L1,T1. h ⊢ ⦃L0, T0⦄ >[g] ⦃L1, T1⦄ → IH_snv_lsubsv h g L1 T1) →
- â\88\80L2,T1. h â\8a¢ â¦\83L0, T0â¦\84 >[g] â¦\83L2, T1â¦\84 â\86\92 â¦\83h, L2â¦\84 â\8a© T1 :[g] →
- ∀L1. h ⊢ L1 ⊩:⊑[g] L2 → ∀T2. ⦃h, L2⦄ ⊢ T1 •*➡*[g] T2 →
+ â\88\80L2,T1. h â\8a¢ â¦\83L0, T0â¦\84 >[g] â¦\83L2, T1â¦\84 â\86\92 â¦\83h, L2â¦\84 â\8a¢ T1 ¡[g] →
+ ∀L1. h ⊢ L1 ¡⊑[g] L2 → ∀T2. ⦃h, L2⦄ ⊢ T1 •*➡*[g] T2 →
∃∃T. ⦃h, L1⦄ ⊢ T1 •*➡*[g] T & L1 ⊢ T2 ➡* T.
#h #g #L0 #T0 #IH4 #IH3 #IH2 #IH1 #L2 #T1 #HLT0 #HT1 #L1 #HL12 #T2 * #T #HT1T #HTT2
lapply (lsubsv_cprs_trans … HL12 … HTT2) -HTT2 #HTT2