-lemma lsstas_fpbg: ∀h,g,G,L,T1,T2,l2. ⦃G, L⦄ ⊢ T1 •*[h, g, l2] T2 → (T1 = T2 → ⊥) →
- ∀l1. l2 ≤ l1 → ⦃G, L⦄ ⊢ T1 ▪[h, g] l1 → ⦃G, L, T1⦄ >[h, g] ⦃G, L, T2⦄.
-#h #g #G #L #T1 #T2 #l2 #H @(lsstas_ind_dx … H) -l2 -T2
-[ #H elim H //
-| #l2 #T #T2 #HT1 #HT2 #IHT1 #HT12 #l1 #Hl21
- elim (term_eq_dec T1 T) #H destruct [ -IHT1 |]
- [ elim (le_inv_plus_l … Hl21) -Hl21 #_ #Hl1
- >(plus_minus_m_m … Hl1) -Hl1 /3 width=5 by ssta_fpbc, fpbg_inj/
- | #Hl1 >commutative_plus in Hl21; #Hl21
- elim (le_inv_plus_l … Hl21) -Hl21 #Hl12 #Hl21
- lapply (lsstas_da_conf … HT1 … Hl1) -HT1
- >(plus_minus_m_m … Hl12) -Hl12
- /4 width=5 by ssta_fpb, fpbg_strap1/
- ]
-]
-qed.
+lemma lstas_fpbg: ∀h,g,G,L,T1,T2,l2. ⦃G, L⦄ ⊢ T1 •*[h, l2] T2 → (T1 = T2 → ⊥) →
+ ∀l1. l2 ≤ l1 → ⦃G, L⦄ ⊢ T1 ▪[h, g] l1 → ⦃G, L, T1⦄ >≡[h, g] ⦃G, L, T2⦄.
+/5 width=5 by fpbc_fpbg, fpbu_fpbc, lstas_fpbu/ qed.
+
+lemma sta_fpbg: ∀h,g,G,L,T1,T2,l. ⦃G, L⦄ ⊢ T1 ▪[h, g] l+1 →
+ ⦃G, L⦄ ⊢ T1 •[h] T2 → ⦃G, L, T1⦄ >≡[h, g] ⦃G, L, T2⦄.
+/4 width=2 by fpbc_fpbg, fpbu_fpbc, sta_fpbu/ qed.