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14
15 include "basic_2/reducibility/ltpr_ltpss_sn.ma".
16 include "basic_2/reducibility/ltpr_ltpr.ma".
17 include "basic_2/reducibility/lfpr.ma".
18
19 (* FOCALIZED PARALLEL REDUCTION ON LOCAL ENVIRONMENTS ***********************)
20
21 (* Main properties **********************************************************)
22
23 theorem lfpr_conf: ∀L0,L1,L2. ⦃L0⦄ ➡ ⦃L1⦄ → ⦃L0⦄ ➡ ⦃L2⦄ →
24                    ∃∃L. ⦃L1⦄ ➡ ⦃L⦄ & ⦃L2⦄ ➡ ⦃L⦄.
25 #K0 #L1 #L2 * #K1 #HK01 #HKL1 * #K2 #HK02 #HKL2
26 lapply (ltpr_fwd_length … HK01) #H
27 >(ltpr_fwd_length … HK02) in H; #H
28 elim (ltpr_conf … HK01 … HK02) -K0 #K #HK1 #HK2
29 lapply (ltpss_sn_fwd_length … HKL1) #H1
30 lapply (ltpss_sn_fwd_length … HKL2) #H2
31 >H1 in HKL1 H; -H1 #HKL1
32 >H2 in HKL2; -H2 #HKL2 #H
33 elim (ltpr_ltpss_sn_conf … HKL1 … HK1) -K1 #K1 #HK1 #HLK1
34 elim (ltpr_ltpss_sn_conf … HKL2 … HK2) -K2 #K2 #HK2 #HLK2
35 elim (ltpss_sn_conf … HK1 … HK2) -K #K #HK1 #HK2
36 lapply (ltpr_fwd_length … HLK1) #H1
37 lapply (ltpr_fwd_length … HLK2) #H2
38 /3 width=5/
39 qed.