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15 include "basic_2/reduction/llpx_ldrop.ma".
16 include "basic_2/computation/cpxs_cpxs.ma".
18 (* CONTEXT-SENSITIVE EXTENDED PARALLEL COMPUTATION ON TERMS *****************)
20 (* Properties on lazy sn reduction on local environments ********************)
22 lemma cpxs_llpx_conf: ∀h,g,G. s_r_confluent1 … (cpxs h g G) (llpx h g G 0).
23 /3 width=5 by llpx_cpx_conf, s_r_conf1_LTC1/ qed-.
25 lemma llpx_cpx_trans: ∀h,g,G. s_r_transitive … (cpx h g G) (llpx h g G 0).
26 #h #g #G #L2 #T1 #T2 #HT12 elim HT12 -G -L2 -T1 -T2
28 | /3 width=2 by cpx_cpxs, cpx_sort/
29 | #I #G #L2 #K2 #V0 #V2 #W2 #i #HLK2 #_ #HVW2 #IHV02 #L1 #HL12
30 elim (llpx_inv_lref_ge_dx … HL12 … HLK2) -L2
31 /5 width=8 by cpxs_delta, cpxs_strap2, llpx_cpx_conf/
32 | #a #I #G #L2 #V1 #V2 #T1 #T2 #_ #_ #IHV12 #IHT12 #L1 #HL12
33 elim (llpx_inv_bind_O … HL12) -HL12 /4 width=1 by cpxs_bind/
34 | #I #G #L2 #V1 #V2 #T1 #T2 #_ #_ #IHV12 #IHT12 #L1 #HL12
35 elim (llpx_inv_flat … HL12) -HL12 /3 width=1 by cpxs_flat/
36 | #G #L2 #V2 #T1 #T #T2 #_ #HT2 #IHT1 #L1 #HL12
37 elim (llpx_inv_bind_O … HL12) /3 width=3 by cpxs_zeta/
38 | #G #L2 #V2 #T1 #T2 #HT12 #IHT12 #L1 #HL12
39 elim (llpx_inv_flat … HL12) /3 width=1 by cpxs_tau/
40 | #G #L2 #V1 #V2 #T2 #HV12 #IHV12 #L1 #HL12
41 elim (llpx_inv_flat … HL12) /3 width=1 by cpxs_ti/
42 | #a #G #L2 #V1 #V2 #W1 #W2 #T1 #T2 #_ #_ #_ #IHV12 #IHW12 #IHT12 #L1 #HL12
43 elim (llpx_inv_flat … HL12) -HL12 #HV1 #HL12
44 elim (llpx_inv_bind_O … HL12) /3 width=3 by cpxs_beta/
45 | #a #G #L2 #V1 #V #V2 #W1 #W2 #T1 #T2 #_ #HV2 #_ #_ #IHV1 #IHW12 #IHT12 #L1 #HL12
46 elim (llpx_inv_flat … HL12) -HL12 #HV1 #HL12
47 elim (llpx_inv_bind_O … HL12) /3 width=3 by cpxs_theta/
51 lemma llpx_cpxs_trans: ∀h,g,G. s_rs_transitive … (cpx h g G) (llpx h g G 0).
52 #h #g #G @s_r_trans_LTC1 /2 width=3 by llpx_cpx_trans, llpx_cpx_conf/ (**) (* full auto fails here but works in cprs_cprs *)