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15 include "basic_2/substitution/cpys_alt.ma".
16 include "basic_2/reduction/cpx.ma".
18 (* CONTEXT-SENSITIVE EXTENDED PARALLEL REDUCTION FOR TERMS ******************)
20 (* Properties on context-sensitive extended multiple substitution for terms *)
22 lemma cpys_cpx: ∀h,g,G,L,T1,T2,d,e. ⦃G, L⦄ ⊢ T1 ▶*×[d, e] T2 → ⦃G, L⦄ ⊢ T1 ➡[h, g] T2.
23 #h #g #G #L #T1 #T2 #d #e #H @(cpys_ind_alt … H) -G -L -T1 -T2 -d -e
24 /2 width=7 by cpx_delta, cpx_bind, cpx_flat/
27 lemma cpy_cpx: ∀h,g,G,L,T1,T2,d,e. ⦃G, L⦄ ⊢ T1 ▶×[d, e] T2 → ⦃G, L⦄ ⊢ T1 ➡[h, g] T2.
28 /3 width=3 by cpy_cpys, cpys_cpx/ qed.