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4 (* ||A|| A project by Andrea Asperti *)
6 (* ||I|| Developers: *)
7 (* ||T|| The HELM team. *)
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15 include "basic_2/computation/cpds.ma".
16 include "basic_2/equivalence/cpcs_cpcs.ma".
17 include "basic_2/equivalence/cpes.ma".
19 (* DECOMPOSED EXTENDED PARALLEL EQUIVALENCE FOR TERMS ***********************)
21 (* Advanced properties ******************************************************)
23 lemma cpds_cpes_dx: ∀h,g,G,L,T1,T2. ⦃G, L⦄ ⊢ T1 •*➡*[h, g] T2 → ⦃G, L⦄ ⊢ T1 •*⬌*[h, g] T2.
24 #h #g #G #L #T1 #T2 * /3 width=7 by cpcs_cprs_dx, ex4_3_intro/
27 (* Advanced inversion lemmas ************************************************)
29 lemma cpes_inv_abst2: ∀h,g,a,G,L,W1,T1,T. ⦃G, L⦄ ⊢ T •*⬌*[h, g] ⓛ{a}W1.T1 →
30 ∃∃W2,T2. ⦃G, L⦄ ⊢ T •*➡*[h, g] ⓛ{a}W2.T2 & ⦃G, L⦄ ⊢ ⓛ{a}W1.T1 ➡* ⓛ{a}W2.T2.
31 #h #g #a #G #L #W1 #T1 #T * #T0 #l #l0 #Hl0 #Hl #HT0 #H
32 elim (cpcs_inv_abst2 … H) -H /3 width=7 by ex4_3_intro, ex2_2_intro/