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4 (* ||A|| A project by Andrea Asperti *)
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15 include "basic_2/rt_computation/lpxs_lpx.ma".
17 (* UNBOUND PARALLEL RT-COMPUTATION FOR FULL LOCAL ENVIRONMENTS **************)
19 (* Properties with context-sensitive extended rt-computation for terms ******)
21 (* Basic_2A1: was: cpxs_bind2 *)
22 lemma cpxs_bind_dx (h) (G): ∀L,V1,V2. ⦃G, L⦄ ⊢ V1 ⬈*[h] V2 →
23 ∀I,T1,T2. ⦃G, L.ⓑ{I}V2⦄ ⊢ T1 ⬈*[h] T2 →
24 ∀p. ⦃G, L⦄ ⊢ ⓑ{p,I}V1.T1 ⬈*[h] ⓑ{p,I}V2.T2.
25 /4 width=5 by lpxs_cpxs_trans, lpxs_pair, cpxs_bind/ qed.
27 (* Inversion lemmas with context-sensitive ext rt-computation for terms *****)
29 lemma cpxs_inv_abst1 (h) (G): ∀p,L,V1,T1,U2. ⦃G, L⦄ ⊢ ⓛ{p}V1.T1 ⬈*[h] U2 →
30 ∃∃V2,T2. ⦃G, L⦄ ⊢ V1 ⬈*[h] V2 & ⦃G, L.ⓛV1⦄ ⊢ T1 ⬈*[h] T2 &
32 #h #G #p #L #V1 #T1 #U2 #H @(cpxs_ind … H) -U2 /2 width=5 by ex3_2_intro/
33 #U0 #U2 #_ #HU02 * #V0 #T0 #HV10 #HT10 #H destruct
34 elim (cpx_inv_abst1 … HU02) -HU02 #V2 #T2 #HV02 #HT02 #H destruct
35 lapply (lpxs_cpx_trans … HT02 (L.ⓛV1) ?)
36 /3 width=5 by lpxs_pair, cpxs_trans, cpxs_strap1, ex3_2_intro/
39 lemma cpxs_inv_abbr1 (h) (G): ∀p,L,V1,T1,U2. ⦃G, L⦄ ⊢ ⓓ{p}V1.T1 ⬈*[h] U2 →
40 ∨∨ ∃∃V2,T2. ⦃G, L⦄ ⊢ V1 ⬈*[h] V2 & ⦃G, L.ⓓV1⦄ ⊢ T1 ⬈*[h] T2 &
42 | ∃∃T2. ⦃G, L.ⓓV1⦄ ⊢ T1 ⬈*[h] T2 & ⬆*[1] U2 ≘ T2 & p = Ⓣ.
43 #h #G #p #L #V1 #T1 #U2 #H @(cpxs_ind … H) -U2 /3 width=5 by ex3_2_intro, or_introl/
45 [ #V0 #T0 #HV10 #HT10 #H destruct
46 elim (cpx_inv_abbr1 … HU02) -HU02 *
47 [ #V2 #T2 #HV02 #HT02 #H destruct
48 lapply (lpxs_cpx_trans … HT02 (L.ⓓV1) ?)
49 /4 width=5 by lpxs_pair, cpxs_trans, cpxs_strap1, ex3_2_intro, or_introl/
51 lapply (lpxs_cpx_trans … HT02 (L.ⓓV1) ?) -HT02
52 /4 width=3 by lpxs_pair, cpxs_trans, ex3_intro, or_intror/
55 elim (cpx_lifts_sn … HU02 (Ⓣ) … (L.ⓓV1) … HU01) -U0 /3 width=3 by drops_refl, drops_drop/ #U #HU2 #HU1
56 /4 width=3 by cpxs_strap1, ex3_intro, or_intror/