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4 (* ||A|| A project by Andrea Asperti *)
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15 include "basic_2/computation/fprs_cprs.ma".
16 include "basic_2/computation/lfprs_fprs.ma".
17 include "basic_2/equivalence/fpcs_fpcs.ma".
18 include "basic_2/equivalence/lfpcs_lfpcs.ma".
20 (* FOCALIZED PARALLEL EQUIVALENCE ON LOCAL ENVIRONMENTS *********************)
22 (* Inversion lemmas on context-free parallel equivalence for closures *******)
24 lemma lfpcs_inv_fpcs: ∀L1,L2. ⦃L1⦄ ⬌* ⦃L2⦄ → ∀T. ⦃L1, T⦄ ⬌* ⦃L2, T⦄.
26 elim (lfpcs_inv_lfprs … HL12) -HL12 #L #HL1 #HL2
27 lapply (lfprs_inv_fprs … HL1 T) -HL1
28 lapply (lfprs_inv_fprs … HL2 T) -HL2 /2 width=4/
31 (* Properties on context-free parallel equivalence for closures *************)
33 lemma fpcs_lfpcs: ∀L1,L2,T1,T2. ⦃L1, T1⦄ ⬌* ⦃L2, T2⦄ → ⦃L1⦄ ⬌* ⦃L2⦄.
35 elim (fpcs_inv_fprs … HT12) -HT12 /3 width=5 by fprs_lfprs, lfprs_div/ (**) (* auto too slow without trace *)
38 lemma fpcs_lift: ∀K1,K2,T1,T2. ⦃K1, T1⦄ ⬌* ⦃K2, T2⦄ →
39 ∀L1,L2. ⦃L1⦄ ⬌* ⦃L2⦄ →
40 ∀d,e. ⇩[d, e] L1 ≡ K1 → ⇩[d, e] L2 ≡ K2 →
41 ∀U1,U2. ⇧[d, e] T1 ≡ U1 → ⇧[d, e] T2 ≡ U2 →
43 #K1 #K2 #T1 #T2 #HT12 #L1 #L2 #HL12 #d #e #HLK1 #HLK2 #U1 #U2 #HTU1 #HTU2
44 elim (fpcs_inv_fprs … HT12) -HT12 #K #T #HT1 #HT2
45 elim (lift_total T d e) #U #HTU
46 elim (fprs_lift … HT1 … HLK1 … HTU1 HTU) -K1 -T1 #K1 #HU1 #_
47 elim (fprs_lift … HT2 … HLK2 … HTU2 HTU) -K2 -T2 -T #K2 #HU2 #_ -K -d -e
48 lapply (lfpcs_lfprs_conf K1 … HL12) -HL12 /2 width=3/ #H
49 lapply (lfpcs_lfprs_strap1 … H K2 ?) -H /2 width=3/ #HK12
50 lapply (lfpcs_inv_fpcs … HK12 U) -HK12 #HU
51 /3 width=4 by fpcs_fprs_strap2, fpcs_fprs_div/