X-Git-Url: http://matita.cs.unibo.it/gitweb/?a=blobdiff_plain;f=matita%2Fmatita%2Fcontribs%2Flambdadelta%2Fbasic_2%2Fdynamic%2Fsnv_lstas_lpr.ma;h=ed9b4e2fa73fb8042f3214b340ee7b18b728be1d;hb=1083ac3b1acac5f1ac1fa40a9a417dd9d268dced;hp=5615c0fdf8defd10670d973c0a11f97d44909e5b;hpb=52e675f555f559c047d5449db7fc89a51b977d35;p=helm.git diff --git a/matita/matita/contribs/lambdadelta/basic_2/dynamic/snv_lstas_lpr.ma b/matita/matita/contribs/lambdadelta/basic_2/dynamic/snv_lstas_lpr.ma index 5615c0fdf..ed9b4e2fa 100644 --- a/matita/matita/contribs/lambdadelta/basic_2/dynamic/snv_lstas_lpr.ma +++ b/matita/matita/contribs/lambdadelta/basic_2/dynamic/snv_lstas_lpr.ma @@ -12,121 +12,111 @@ (* *) (**************************************************************************) -include "basic_2/computation/cpds_cpds.ma". include "basic_2/dynamic/snv_aaa.ma". -include "basic_2/dynamic/snv_cpcs.ma". +include "basic_2/dynamic/snv_scpes.ma". include "basic_2/dynamic/lsubsv_lstas.ma". (* STRATIFIED NATIVE VALIDITY FOR TERMS *************************************) (* Properties on sn parallel reduction for local environments ***************) -fact lstas_cpr_lpr_aux: ∀h,g,G0,L0,T0. - (∀G1,L1,T1. ⦃G0, L0, T0⦄ >≡[h, g] ⦃G1, L1, T1⦄ → IH_snv_lstas h g G1 L1 T1) → - (∀G1,L1,T1. ⦃G0, L0, T0⦄ >≡[h, g] ⦃G1, L1, T1⦄ → IH_snv_cpr_lpr h g G1 L1 T1) → - (∀G1,L1,T1. ⦃G0, L0, T0⦄ >≡[h, g] ⦃G1, L1, T1⦄ → IH_da_cpr_lpr h g G1 L1 T1) → - (∀G1,L1,T1. ⦃G0, L0, T0⦄ >≡[h, g] ⦃G1, L1, T1⦄ → IH_lstas_cpr_lpr h g G1 L1 T1) → - ∀G1,L1,T1. G0 = G1 → L0 = L1 → T0 = T1 → IH_lstas_cpr_lpr h g G1 L1 T1. -#h #g #G0 #L0 #T0 #IH4 #IH3 #IH2 #IH1 #G1 #L1 * * [|||| * ] -[ #k #_ #_ #_ #_ #l1 #l2 #_ #_ #X2 #H2 #X3 #H3 #L2 #_ -IH4 -IH3 -IH2 -IH1 +fact lstas_cpr_lpr_aux: ∀h,o,G0,L0,T0. + (∀G1,L1,T1. ⦃G0, L0, T0⦄ >≛[h, o] ⦃G1, L1, T1⦄ → IH_snv_lstas h o G1 L1 T1) → + (∀G1,L1,T1. ⦃G0, L0, T0⦄ >≛[h, o] ⦃G1, L1, T1⦄ → IH_snv_cpr_lpr h o G1 L1 T1) → + (∀G1,L1,T1. ⦃G0, L0, T0⦄ >≛[h, o] ⦃G1, L1, T1⦄ → IH_da_cpr_lpr h o G1 L1 T1) → + (∀G1,L1,T1. ⦃G0, L0, T0⦄ >≛[h, o] ⦃G1, L1, T1⦄ → IH_lstas_cpr_lpr h o G1 L1 T1) → + ∀G1,L1,T1. G0 = G1 → L0 = L1 → T0 = T1 → IH_lstas_cpr_lpr h o G1 L1 T1. +#h #o #G0 #L0 #T0 #IH4 #IH3 #IH2 #IH1 #G1 #L1 * * [|||| * ] +[ #s #_ #_ #_ #_ #d1 #d2 #_ #_ #X2 #H2 #X3 #H3 #L2 #_ -IH4 -IH3 -IH2 -IH1 >(lstas_inv_sort1 … H2) -X2 >(cpr_inv_sort1 … H3) -X3 /2 width=3 by ex2_intro/ -| #i #HG0 #HL0 #HT0 #H1 #l1 #l2 @(nat_ind_plus … l2) -l2 [ #_ | #l2 #_ #Hl21 ] #Hl1 #X2 #H2 #X3 #H3 #L2 #HL12 destruct -IH4 -IH3 - [ lapply (lstas_inv_O … H2) -H2 #H destruct -IH1 -H1 -l1 /4 width=5 by lpr_cpcs_conf, cpr_cpcs_dx, ex2_intro/ ] +| #i #HG0 #HL0 #HT0 #H1 #d1 #d2 #Hd21 #Hd1 #X2 #H2 #X3 #H3 #L2 #HL12 destruct -IH4 -IH3 elim (snv_inv_lref … H1) -H1 #I0 #K0 #X0 #HK0 #HX0 - elim (da_inv_lref … Hl1) -Hl1 * #K1 [ #V1 | #W1 #l0 ] #HLK1 [ #HVl1 | #HWl1 #H destruct ] + elim (da_inv_lref … Hd1) -Hd1 * #K1 [ #V1 | #W1 #d ] #HLK1 [ #HVd1 | #HWd1 #H destruct ] lapply (drop_mono … HK0 … HLK1) -HK0 #H destruct - elim (lstas_inv_lref1 … H2) -H2 * #K0 #V0 #W0 [2,4: #X0 ] #HK0 [1,2: #_ -X0 ] #HVW0 #HX2 + elim (lstas_inv_lref1 … H2) -H2 * #K0 #V0 #X0 [3,6: #d0 ] #HK0 #HVX0 [1,2: #HX02 #H |3,5: #HX02 |4,6: #H1 #H2 ] destruct lapply (drop_mono … HK0 … HLK1) -HK0 #H destruct - [ lapply (le_plus_to_le_r … Hl21) -Hl21 #Hl21 ] + [ lapply (le_plus_to_le_c … Hd21) -Hd21 #Hd21 |3: -Hd21 ] lapply (fqup_lref … G1 … HLK1) #HKV1 elim (lpr_drop_conf … HLK1 … HL12) -HL12 #X #H #HLK2 - elim (lpr_inv_pair1 … H) -H #K2 [ #W2 | #V2 ] #HK12 [ #HW12 | #HV12 ] #H destruct + elim (lpr_inv_pair1 … H) -H #K2 [ #W2 | #W2 | #V2 ] #HK12 [ #HW12 | #HW12 | #HV12 ] #H destruct lapply (drop_fwd_drop2 … HLK2) #H2 elim (cpr_inv_lref1 … H3) -H3 - [1,3: #H destruct -HLK1 - |2,4: * #K0 #V0 #X0 #H #HVX0 #HX0 - lapply (drop_mono … H … HLK1) -H -HLK1 #H destruct + [1,3,5: #H destruct -HLK1 + |2,4,6: * #K #V #X #H #HVX #HX3 + lapply (drop_mono … H … HLK1) -H -HLK1 #H destruct ] - [ lapply (IH2 … HWl1 … HW12 … HK12) /2 width=1 by fqup_fpbg/ -IH2 #H - elim (da_inv_sta … H) -H - elim (IH1 … HWl1 … HVW0 … HW12 … HK12) -IH1 -HVW0 /2 width=1 by fqup_fpbg/ #V2 #HWV2 #HV2 + [ lapply (IH2 … HWd1 … HW12 … HK12) /2 width=1 by fqup_fpbg/ -IH2 #H + elim (da_lstas … H d0) -H + elim (IH1 … HWd1 … HVX0 … HW12 … HK12) -IH1 -HVX0 /2 width=1 by fqup_fpbg/ #V2 #HWV2 #HV2 elim (lift_total V2 0 (i+1)) - /3 width=12 by cpcs_lift, lstas_ldec, ex2_intro/ - | elim (IH1 … HVl1 … HVW0 … HV12 … HK12) -IH1 -HVl1 -HVW0 -HV12 -HK12 -IH2 /2 width=1 by fqup_fpbg/ #W2 #HVW2 #HW02 + /3 width=12 by cpcs_lift, lstas_succ, ex2_intro/ + | elim (IH1 … HWd1 … HVX0 … HW12 … HK12) -IH1 -HVX0 + /3 width=5 by fqup_fpbg, lstas_zero, ex2_intro/ + | elim (IH1 … HVd1 … HVX0 … HV12 … HK12) -IH1 -HVd1 -HVX0 -HV12 -HK12 -IH2 /2 width=1 by fqup_fpbg/ #W2 #HVW2 #HW02 elim (lift_total W2 0 (i+1)) /4 width=12 by cpcs_lift, lstas_ldef, ex2_intro/ - | elim (IH1 … HVl1 … HVW0 … HVX0 … HK12) -IH1 -HVl1 -HVW0 -HVX0 -HK12 -IH2 -V2 /2 width=1 by fqup_fpbg/ -l1 #W2 #HXW2 #HW02 + | elim (IH1 … HVd1 … HVX0 … HVX … HK12) -IH1 -HVd1 -HVX0 -HVX -HK12 -IH2 -V2 /2 width=1 by fqup_fpbg/ -d1 #W2 #HXW2 #HW02 elim (lift_total W2 0 (i+1)) /3 width=12 by cpcs_lift, lstas_lift, ex2_intro/ ] | #p #_ #_ #HT0 #H1 destruct -IH4 -IH3 -IH2 -IH1 elim (snv_inv_gref … H1) -| #a #I #V1 #T1 #HG0 #HL0 #HT0 #H1 #l1 #l2 #Hl21 #Hl1 #X2 #H2 #X3 #H3 #L2 #HL12 destruct -IH4 -IH3 -IH2 +| #a #I #V1 #T1 #HG0 #HL0 #HT0 #H1 #d1 #d2 #Hd21 #Hd1 #X2 #H2 #X3 #H3 #L2 #HL12 destruct -IH4 -IH3 -IH2 elim (snv_inv_bind … H1) -H1 #_ #HT1 - lapply (da_inv_bind … Hl1) -Hl1 #Hl1 + lapply (da_inv_bind … Hd1) -Hd1 #Hd1 elim (lstas_inv_bind1 … H2) -H2 #U1 #HTU1 #H destruct elim (cpr_inv_bind1 … H3) -H3 * [ #V2 #T2 #HV12 #HT12 #H destruct - elim (IH1 … Hl1 … HTU1 … HT12 (L2.ⓑ{I}V2)) -IH1 -Hl1 -HTU1 -HT12 /2 width=1 by fqup_fpbg, lpr_pair/ -T1 + elim (IH1 … Hd1 … HTU1 … HT12 (L2.ⓑ{I}V2)) -IH1 -Hd1 -HTU1 -HT12 /2 width=1 by fqup_fpbg, lpr_pair/ -T1 /4 width=5 by cpcs_bind2, lpr_cpr_conf, lstas_bind, ex2_intro/ | #T3 #HT13 #HXT3 #H1 #H2 destruct - elim (IH1 … Hl1 … HTU1 … HT13 (L2.ⓓV1)) -IH1 -Hl1 -HTU1 -HT13 /2 width=1 by fqup_fpbg, lpr_pair/ -T1 -HL12 #U3 #HTU3 #HU13 + elim (IH1 … Hd1 … HTU1 … HT13 (L2.ⓓV1)) -IH1 -Hd1 -HTU1 -HT13 /2 width=1 by fqup_fpbg, lpr_pair/ -T1 -HL12 #U3 #HTU3 #HU13 elim (lstas_inv_lift1 … HTU3 L2 … HXT3) -T3 /5 width=8 by cpcs_cpr_strap1, cpcs_bind1, cpr_zeta, drop_drop, ex2_intro/ ] -| #V1 #T1 #HG0 #HL0 #HT0 #H1 #l1 #l2 #Hl21 #Hl1 #X2 #H2 #X3 #H3 #L2 #HL12 destruct - elim (snv_inv_appl … H1) -H1 #a #W1 #W10 #U10 #l0 #HV1 #HT1 #Hl0 #HVW1 #HW10 #HTU10 - lapply (da_inv_flat … Hl1) -Hl1 #Hl1 - elim (lstas_inv_appl1 … H2) -H2 #U1 #HTU1 #H destruct +| #V1 #T1 #HG0 #HL0 #HT0 #H1 #d1 #d2 #Hd21 #Hd1 #X2 #H2 #X3 #H3 #L2 #HL12 destruct + elim (snv_inv_appl … H1) -H1 #a #W1 #U1 #d0 #HV1 #HT1 #HVW1 #HTU1 + lapply (da_inv_flat … Hd1) -Hd1 #Hd1 + elim (lstas_inv_appl1 … H2) -H2 #X #HT1U #H destruct elim (cpr_inv_appl1 … H3) -H3 * - [ #V2 #T2 #HV12 #HT12 #H destruct -a -l0 -W1 -W10 -U10 -HV1 -IH4 -IH3 -IH2 - elim (IH1 … Hl1 … HTU1 … HT12 … HL12) -IH1 -Hl1 -HTU1 + [ #V2 #T2 #HV12 #HT12 #H destruct -a -d0 -W1 -U1 -HV1 -IH4 -IH3 -IH2 + elim (IH1 … Hd1 … HT1U … HT12 … HL12) -IH1 -Hd1 -HT1U /4 width=5 by fqup_fpbg, cpcs_flat, lpr_cpr_conf, lstas_appl, ex2_intro/ | #b #V2 #W2 #W3 #T2 #T3 #HV12 #HW23 #HT23 #H1 #H2 destruct elim (snv_inv_bind … HT1) -HT1 #HW2 #HT2 - lapply (da_inv_bind … Hl1) -Hl1 #Hl1 - elim (lstas_inv_bind1 … HTU1) -HTU1 #U2 #HTU2 #H destruct - elim (cpds_inv_abst1 … HTU10) -HTU10 #W0 #U0 #HW20 #_ #H destruct - lapply (cprs_div … HW10 … HW20) -W0 #HW12 - lapply (da_sta_conf … HVW1 … Hl0) (plus_minus_k_k d 1) in HV1d; // -H #HV1d + lapply (scpes_cpr_lpr_aux … IH2 IH1 … H21 … HW23 … HV12 … HL12) -H21 /2 width=1 by fqup_fpbg/ #H32 lapply (IH3 … HW23 … HL12) /2 width=1 by fqup_fpbg/ #HW3 - lapply (IH2 … Hl … HW23 … HL12) /2 width=1 by fqup_fpbg/ #HW3l - elim (IH1 … Hl1 … HTU2 … HT23 (L2.ⓛW3)) -HTU2 /2 width=1 by fqup_fpbg, lpr_pair/ #U3 #HTU3 #HU23 - lapply (cpcs_cpr_strap1 … HW12 … HW23) #H - lapply (lpr_cpcs_conf … HL12 … H) -H #H - lapply (cpcs_canc_sn … HW14 H) -H #HW43 - elim (lsubsv_lstas_trans … g … HTU3 … Hl21 … (L2.ⓓⓝW3.V2)) -HTU3 - [ #U4 #HT3U4 #HU43 -HW12 -HW3 -HW3l -W4 -IH2 -IH3 -IH4 + lapply (IH3 … HV12 … HL12) /2 width=1 by fqup_fpbg/ #HV2 + lapply (IH2 … HW2d … HW23 … HL12) /2 width=1 by fqup_fpbg/ -HW2 -HW2d #HW3d + lapply (IH2 … HV1d … HV12 … HL12) /2 width=1 by fqup_fpbg/ -HV1 -HV1d #HV2d + elim (IH1 … Hd1 … HT2U … HT23 (L2.ⓛW3)) -HT2U /2 width=1 by fqup_fpbg, lpr_pair/ #U3 #HTU3 #HU23 + elim (lsubsv_lstas_trans … o … HTU3 … Hd21 … (L2.ⓓⓝW3.V2)) -HTU3 + [ #U4 #HT3U4 #HU43 -IH1 -IH2 -IH3 -IH4 -d -d1 -HW3 -HV2 -HT2 @(ex2_intro … (ⓓ{b}ⓝW3.V2.U4)) /2 width=1 by lstas_bind/ -HT3U4 @(cpcs_canc_dx … (ⓓ{b}ⓝW3.V2.U3)) /2 width=1 by cpcs_bind_dx/ -HU43 @(cpcs_cpr_strap1 … (ⓐV2.ⓛ{b}W3.U3)) /2 width=1 by cpr_beta/ /4 width=3 by cpcs_flat, cpcs_bind2, lpr_cpr_conf/ | -U3 - @(lsubsv_abbr … l) /3 width=7 by fqup_fpbg/ - #W #W0 #l0 #Hl0 #HV2W #HW30 - lapply (lstas_sta_conf_pos … HV2W4 … HV2W) -HV2W #HW4W - @(lstas_cpcs_lpr_aux … IH3 IH2 IH1 … Hl0 … HW4W … Hl0 … HW30 … HW43) // - [ /3 width=9 by fpbg_fpbs_trans, fqup_fpbg, cpr_lpr_sta_fpbs/ - | /3 width=5 by fpbg_fpbs_trans, fqup_fpbg, cpr_lpr_fpbs/ - ] + @(lsubsv_beta … (d-1)) /3 width=7 by fqup_fpbg/ + @shnv_cast [1,2: // ] #d0 #Hd0 + lapply (scpes_le_aux … IH4 IH3 IH2 IH1 … HW3d … HV2d … d0 … H32) -IH4 -IH3 -IH2 -IH1 -HW3d -HV2d -H32 + /3 width=5 by fpbg_fpbs_trans, fqup_fpbg, cpr_lpr_fpbs, le_S_S/ | -IH1 -IH3 -IH4 /3 width=9 by fqup_fpbg, lpr_pair/ ] - | #b #V0 #V2 #W0 #W2 #T0 #T2 #HV10 #HV02 #HW02 #HT02 #H1 #H2 destruct -a -l0 -W1 -W10 -HV1 -IH4 -IH3 -IH2 + | #b #V0 #V2 #W0 #W2 #T0 #T2 #HV10 #HV02 #HW02 #HT02 #H1 #H2 destruct -a -d0 -W1 -HV1 -IH4 -IH3 -IH2 elim (snv_inv_bind … HT1) -HT1 #_ #HT0 - lapply (da_inv_bind … Hl1) -Hl1 #Hl1 - elim (lstas_inv_bind1 … HTU1) -HTU1 #U0 #HTU0 #H destruct - elim (IH1 … Hl1 … HTU0 … HT02 (L2.ⓓW2)) -IH1 -Hl1 -HTU0 /2 width=1 by fqup_fpbg, lpr_pair/ -T0 #U2 #HTU2 #HU02 + lapply (da_inv_bind … Hd1) -Hd1 #Hd1 + elim (lstas_inv_bind1 … HT1U) -HT1U #U0 #HTU0 #H destruct + elim (IH1 … Hd1 … HTU0 … HT02 (L2.ⓓW2)) -IH1 -Hd1 -HTU0 /2 width=1 by fqup_fpbg, lpr_pair/ -T0 #U2 #HTU2 #HU02 lapply (lpr_cpr_conf … HL12 … HV10) -HV10 #HV10 lapply (lpr_cpr_conf … HL12 … HW02) -L1 #HW02 lapply (cpcs_bind2 b … HW02 … HU02) -HW02 -HU02 #HU02 @@ -134,17 +124,15 @@ fact lstas_cpr_lpr_aux: ∀h,g,G0,L0,T0. lapply (cpcs_cpr_strap1 … HU02 (ⓓ{b}W2.ⓐV2.U2) ?) /4 width=3 by lstas_appl, lstas_bind, cpr_theta, ex2_intro/ ] -| #W1 #T1 #HG0 #HL0 #HT0 #H1 #l1 #l2 @(nat_ind_plus … l2) -l2 [ #_ | #l2 #_ #Hl21 ] #Hl1 #X2 #H2 #X3 #H3 #L2 #HL12 destruct -IH4 -IH3 -IH2 - [ lapply (lstas_inv_O … H2) -H2 #H destruct -IH1 -H1 -l1 /4 width=5 by lpr_cpcs_conf, cpr_cpcs_dx, ex2_intro/ ] - elim (snv_inv_cast … H1) -H1 #U1 #l #_ #HT1 #_ #_ #_ -U1 -l - lapply (da_inv_flat … Hl1) -Hl1 #Hl1 +| #W1 #T1 #HG0 #HL0 #HT0 #H1 #d1 #d2 #Hd21 #Hd1 #X2 #H2 #X3 #H3 #L2 #HL12 destruct -IH4 -IH3 -IH2 + elim (snv_inv_cast … H1) -H1 #U1 #_ #HT1 #_ #_ -U1 + lapply (da_inv_flat … Hd1) -Hd1 #Hd1 lapply (lstas_inv_cast1 … H2) -H2 #HTU1 elim (cpr_inv_cast1 … H3) -H3 [ * #U2 #T2 #_ #HT12 #H destruct - elim (IH1 … Hl1 … HTU1 … HT12 … HL12) -IH1 -Hl1 -HTU1 -HL12 + elim (IH1 … Hd1 … HTU1 … HT12 … HL12) -IH1 -Hd1 -HTU1 -HL12 /3 width=3 by fqup_fpbg, lstas_cast, ex2_intro/ - | #HT1X3 - elim (IH1 … Hl1 … HTU1 … HT1X3 … HL12) -IH1 -Hl1 -HTU1 -HL12 + | #HT1X3 elim (IH1 … Hd1 … HTU1 … HT1X3 … HL12) -IH1 -Hd1 -HTU1 -HL12 /2 width=3 by fqup_fpbg, ex2_intro/ ] ]