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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/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 (* Basic_2A1: was: cpxs_inv_abbr1 *)
40 lemma cpxs_inv_abbr1_dx (h) (p) (G) (L):
41 ∀V1,T1,U2. ⦃G,L⦄ ⊢ ⓓ{p}V1.T1 ⬈*[h] U2 →
42 ∨∨ ∃∃V2,T2. ⦃G,L⦄ ⊢ V1 ⬈*[h] V2 & ⦃G,L.ⓓV1⦄ ⊢ T1 ⬈*[h] T2 &
44 | ∃∃T2. ⦃G,L.ⓓV1⦄ ⊢ T1 ⬈*[h] T2 & ⬆*[1] U2 ≘ T2 & p = Ⓣ.
45 #h #p #G #L #V1 #T1 #U2 #H
46 @(cpxs_ind … H) -U2 /3 width=5 by ex3_2_intro, or_introl/
48 [ #V0 #T0 #HV10 #HT10 #H destruct
49 elim (cpx_inv_abbr1 … HU02) -HU02 *
50 [ #V2 #T2 #HV02 #HT02 #H destruct
51 lapply (lpxs_cpx_trans … HT02 (L.ⓓV1) ?)
52 /4 width=5 by lpxs_pair, cpxs_trans, cpxs_strap1, ex3_2_intro, or_introl/
53 | #T2 #HT20 #HTU2 #Hp -V0
54 elim (cpx_lifts_sn … HTU2 (Ⓣ) … (L.ⓓV1) … HT20) -T2 [| /3 width=3 by drops_refl, drops_drop/ ] #U0 #HU20 #HTU0
55 /4 width=3 by cpxs_strap1, ex3_intro, or_intror/
58 elim (cpx_lifts_sn … HU02 (Ⓣ) … (L.ⓓV1) … HU01) -U0 [| /3 width=3 by drops_refl, drops_drop/ ] #U #HU2 #HU1
59 /4 width=3 by cpxs_strap1, ex3_intro, or_intror/