-lemma sstas_inv_bind1: ∀h,g,J,L,Y,X,U. ⦃h, L⦄ ⊢ ⓑ{J}Y.X •*[g] U →
- ∃∃Z. ⦃h, L.ⓑ{J}Y⦄ ⊢ X •*[g] Z & U = ⓑ{J}Y.Z.
-/2 width=3/ qed-.
-
-fact sstas_inv_appl1_aux: ∀h,g,L,T,U. ⦃h, L⦄ ⊢ T •*[g] U → ∀X,Y. T = ⓐY.X →
- ∃∃Z. ⦃h, L⦄ ⊢ X •*[g] Z & U = ⓐY.Z.
-#h #g #L #T #U #H @(sstas_ind_alt … H) -T
-[ #U0 #HU0 #X #Y #H destruct
- elim (ssta_inv_appl1 … HU0) -HU0 #X0 #HX0 #H destruct /3 width=3/
-| #T0 #U0 #l #HTU0 #_ #IHU0 #X #Y #H destruct
- elim (ssta_inv_appl1 … HTU0) -HTU0 #X0 #HX0 #H destruct
- elim (IHU0 X0 Y ?) -IHU0 // #X1 #HX01 #H destruct /3 width=4/
-]
+lemma sstas_strap1: ∀h,g,G,L,T1,T2,U2,l. ⦃G, L⦄ ⊢ T1 •*[h, g] T2 → ⦃G, L⦄ ⊢ T2 •[h, g] ⦃l+1, U2⦄ →
+ ⦃G, L⦄ ⊢ T1 •*[h, g] U2.
+/3 width=4 by sstep, ex_intro/ (**) (* auto fails without trace *)