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4 (* ||A|| A project by Andrea Asperti *)
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7 (* ||T|| The HELM team. *)
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15 include "basic_2/computation/scpds_scpds.ma".
16 include "basic_2/equivalence/cpcs_cpcs.ma".
17 include "basic_2/equivalence/scpes.ma".
19 (* STRATIFIED DECOMPOSED PARALLEL EQUIVALENCE FOR TERMS *********************)
21 (* Inversion lemmas on parallel equivalence for terms ***********************)
23 lemma scpes_inv_lstas_eq: ∀h,o,G,L,T1,T2,d1,d2. ⦃G, L⦄ ⊢ T1 •*⬌*[h, o, d1, d2] T2 →
24 ∀U1. ⦃G, L⦄ ⊢ T1 •*[h, d1] U1 →
25 ∀U2. ⦃G, L⦄ ⊢ T2 •*[h, d2] U2 → ⦃G, L⦄ ⊢ U1 ⬌* U2.
26 #h #o #G #L #T1 #T2 #d1 #d2 * #T #HT1 #HT2 #U1 #HTU1 #U2 #HTU2
27 /3 width=8 by scpds_inv_lstas_eq, cprs_div/
30 (* Properties on parallel equivalence for terms *****************************)
32 lemma cpcs_scpes: ∀h,o,G,L,T1,d11. ⦃G, L⦄ ⊢ T1 ▪[h, o] d11 →
33 ∀U1,d12. d12 ≤ d11 → ⦃G, L⦄ ⊢ T1 •*[h, d12] U1 →
34 ∀T2,d21. ⦃G, L⦄ ⊢ T2 ▪[h, o] d21 →
35 ∀U2,d22. d22 ≤ d21 → ⦃G, L⦄ ⊢ T2 •*[h, d22] U2 →
36 ⦃G, L⦄ ⊢ U1 ⬌* U2 → ⦃G, L⦄ ⊢ T1 •*⬌*[h, o, d12, d22] T2.
37 #h #o #G #L #T1 #d11 #HT1 #U1 #d12 #Hd121 #HTU1 #T2 #d21 #HT2 #U2 #d22 #Hd221 #HTU2 #HU12
38 elim (cpcs_inv_cprs … HU12) -HU12 /3 width=6 by scpds_div, ex4_2_intro/