(* Advanced inversion lemmas ************************************************)
-lemma sstas_inv_O: ∀h,g,L,T,U. ⦃G, L⦄ ⊢ T •*[h, g] U →
+lemma sstas_inv_O: ∀h,g,G,L,T,U. ⦃G, L⦄ ⊢ T •*[h, g] U →
∀T0. ⦃G, L⦄ ⊢ T •[h, g] ⦃0, T0⦄ → U = T.
-#h #g #L #T #U #H @(sstas_ind_dx … H) -T //
+#h #g #G #L #T #U #H @(sstas_ind_dx … H) -T //
#T0 #U0 #l0 #HTU0 #_ #_ #T1 #HT01
elim (ssta_mono … HTU0 … HT01) <plus_n_Sm #H destruct
qed-.
(* Advanced properties ******************************************************)
-lemma sstas_strip: ∀h,g,L,T,U1. ⦃G, L⦄ ⊢ T •*[h, g] U1 →
+lemma sstas_strip: ∀h,g,G,L,T,U1. ⦃G, L⦄ ⊢ T •*[h, g] U1 →
∀U2,l. ⦃G, L⦄ ⊢ T •[h, g] ⦃l, U2⦄ →
T = U1 ∨ ⦃G, L⦄ ⊢ U2 •*[h, g] U1.
-#h #g #L #T #U1 #H1 @(sstas_ind_dx … H1) -T /2 width=1/
+#h #g #G #L #T #U1 #H1 @(sstas_ind_dx … H1) -T /2 width=1/
#T #U #l0 #HTU #HU1 #_ #U2 #l #H2
elim (ssta_mono … H2 … HTU) -H2 -HTU #H1 #H2 destruct /2 width=1/
qed-.
(* Main properties **********************************************************)
-theorem sstas_trans: ∀h,g,L,T1,U. ⦃G, L⦄ ⊢ T1 •*[h, g] U →
+theorem sstas_trans: ∀h,g,G,L,T1,U. ⦃G, L⦄ ⊢ T1 •*[h, g] U →
∀T2. ⦃G, L⦄ ⊢ U •*[h, g] T2 → ⦃G, L⦄ ⊢ T1 •*[h, g] T2.
/2 width=3/ qed-.
-theorem sstas_conf: ∀h,g,L,T,U1. ⦃G, L⦄ ⊢ T •*[h, g] U1 →
+theorem sstas_conf: ∀h,g,G,L,T,U1. ⦃G, L⦄ ⊢ T •*[h, g] U1 →
∀U2. ⦃G, L⦄ ⊢ T •*[h, g] U2 →
⦃G, L⦄ ⊢ U1 •*[h, g] U2 ∨ ⦃G, L⦄ ⊢ U2 •*[h, g] U1.
-#h #g #L #T #U1 #H1 @(sstas_ind_dx … H1) -T /2 width=1/
+#h #g #G #L #T #U1 #H1 @(sstas_ind_dx … H1) -T /2 width=1/
#T #U #l #HTU #HU1 #IHU1 #U2 #H2
elim (sstas_strip … H2 … HTU) #H destruct
[ -H2 -IHU1 /3 width=4/