lemma lsubsv_lstas_trans: ∀h,g,G,L2,T,U2,l1. ⦃G, L2⦄ ⊢ T •*[h, l1] U2 →
∀l2. l1 ≤ l2 → ⦃G, L2⦄ ⊢ T ▪[h, g] l2 →
- ∀L1. G ⊢ L1 ¡⫃[h, g] L2 →
+ ∀L1. G ⊢ L1 ⫃¡[h, g] L2 →
∃∃U1. ⦃G, L1⦄ ⊢ T •*[h, l1] U1 & ⦃G, L1⦄ ⊢ U1 ⬌* U2.
#h #g #G #L2 #T #U #l1 #H @(lstas_ind_alt … H) -G -L2 -T -U -l1
[1,2: /2 width=3 by ex2_intro/
lemma lsubsv_sta_trans: ∀h,g,G,L2,T,U2. ⦃G, L2⦄ ⊢ T •[h] U2 →
∀l. ⦃G, L2⦄ ⊢ T ▪[h, g] l+1 →
- ∀L1. G ⊢ L1 ¡⫃[h, g] L2 →
+ ∀L1. G ⊢ L1 ⫃¡[h, g] L2 →
∃∃U1. ⦃G, L1⦄ ⊢ T •[h] U1 & ⦃G, L1⦄ ⊢ U1 ⬌* U2.
#h #g #G #L2 #T #U2 #H #l #HTl #L1 #HL12
elim (lsubsv_lstas_trans … U2 1 … HTl … HL12)