(* Properties on context-sensitive extended multiple substitution for terms *)
-lemma cpys_cpx: ∀h,g,G,L,T1,T2,d,e. ⦃G, L⦄ ⊢ T1 ▶*×[d, e] T2 → ⦃G, L⦄ ⊢ T1 ➡[h, g] T2.
+lemma cpys_cpx: ∀h,g,G,L,T1,T2,d,e. ⦃G, L⦄ ⊢ T1 ▶*[d, e] T2 → ⦃G, L⦄ ⊢ T1 ➡[h, g] T2.
#h #g #G #L #T1 #T2 #d #e #H @(cpys_ind_alt … H) -G -L -T1 -T2 -d -e
/2 width=7 by cpx_delta, cpx_bind, cpx_flat/
qed.
-lemma cpy_cpx: ∀h,g,G,L,T1,T2,d,e. ⦃G, L⦄ ⊢ T1 ▶×[d, e] T2 → ⦃G, L⦄ ⊢ T1 ➡[h, g] T2.
+lemma cpy_cpx: ∀h,g,G,L,T1,T2,d,e. ⦃G, L⦄ ⊢ T1 ▶[d, e] T2 → ⦃G, L⦄ ⊢ T1 ➡[h, g] T2.
/3 width=3 by cpy_cpys, cpys_cpx/ qed.