X-Git-Url: http://matita.cs.unibo.it/gitweb/?a=blobdiff_plain;f=matita%2Fmatita%2Fcontribs%2Flambdadelta%2Fbasic_2%2Fdynamic%2Flsubsv_lstas.ma;h=37aa2a84578bbea39d135f035976b845c976e77c;hb=c2211ba58807254e75c6321cbd688db462d80fd2;hp=0a75b3e961bf0e00a9a5963c86eeaaccf5bca077;hpb=d8ddeb030acbf2246693dc0b65c321ee39e4328b;p=helm.git diff --git a/matita/matita/contribs/lambdadelta/basic_2/dynamic/lsubsv_lstas.ma b/matita/matita/contribs/lambdadelta/basic_2/dynamic/lsubsv_lstas.ma index 0a75b3e96..37aa2a845 100644 --- a/matita/matita/contribs/lambdadelta/basic_2/dynamic/lsubsv_lstas.ma +++ b/matita/matita/contribs/lambdadelta/basic_2/dynamic/lsubsv_lstas.ma @@ -12,58 +12,59 @@ (* *) (**************************************************************************) -include "basic_2/static/da_sta.ma". include "basic_2/static/lsubd_da.ma". include "basic_2/unfold/lstas_alt.ma". -include "basic_2/equivalence/cpcs_cpcs.ma". +include "basic_2/equivalence/cpes_cpcs.ma". include "basic_2/dynamic/lsubsv_lsubd.ma". (* LOCAL ENVIRONMENT REFINEMENT FOR STRATIFIED NATIVE VALIDITY **************) (* Properties on nat-iterated static type assignment ************************) -lemma lsubsv_lstas_trans: ∀h,g,G,L2,T,U2,l1. ⦃G, L2⦄ ⊢ T •*[h, l1] U2 → - ∀l2. l1 ≤ l2 → ⦃G, L2⦄ ⊢ T ▪[h, g] l2 → +lemma lsubsv_lstas_trans: ∀h,g,G,L2,T,U2,l2. ⦃G, L2⦄ ⊢ T •*[h, l2] U2 → + ∀l1. l2 ≤ l1 → ⦃G, L2⦄ ⊢ T ▪[h, g] l1 → ∀L1. G ⊢ L1 ⫃¡[h, g] L2 → - ∃∃U1. ⦃G, L1⦄ ⊢ T •*[h, l1] U1 & ⦃G, L1⦄ ⊢ U1 ⬌* U2. -#h #g #G #L2 #T #U #l1 #H @(lstas_ind_alt … H) -G -L2 -T -U -l1 + ∃∃U1. ⦃G, L1⦄ ⊢ T •*[h, l2] U1 & ⦃G, L1⦄ ⊢ U1 ⬌* U2. +#h #g #G #L2 #T #U #l2 #H @(lstas_ind_alt … H) -G -L2 -T -U -l2 [1,2: /2 width=3 by ex2_intro/ -| #G #L2 #K2 #X #Y #U #i #l1 #HLK2 #_ #HYU #IHXY #l2 #Hl12 #Hl2 #L1 #HL12 - elim (da_inv_lref … Hl2) -Hl2 * #K0 #V0 [| #l0 ] #HK0 #HV0 +| #G #L2 #K2 #X #Y #U #i #l2 #HLK2 #_ #HYU #IHXY #l1 #Hl21 #Hl1 #L1 #HL12 + elim (da_inv_lref … Hl1) -Hl1 * #K0 #V0 [| #l0 ] #HK0 #HV0 lapply (drop_mono … HK0 … HLK2) -HK0 #H destruct elim (lsubsv_drop_O1_trans … HL12 … HLK2) -L2 #X #H #HLK1 elim (lsubsv_inv_pair2 … H) -H * #K1 [ | -HYU -IHXY -HLK1 ] [ #HK12 #H destruct - elim (IHXY … Hl12 HV0 … HK12) -K2 -l2 #T #HXT #HTY + elim (IHXY … Hl21 HV0 … HK12) -K2 -l1 #T #HXT #HTY lapply (drop_fwd_drop2 … HLK1) #H elim (lift_total T 0 (i+1)) /3 width=12 by lstas_ldef, cpcs_lift, ex2_intro/ - | #V #l0 #_ #_ #_ #_ #_ #_ #_ #H destruct + | #V #l0 #_ #_ #_ #_ #_ #H destruct ] -| #G #L2 #K2 #X #Y #Y0 #U #i #l1 #HLK2 #HXY0 #_ #HYU #IHXY #l2 #Hl12 #Hl2 #L1 #HL12 - elim (da_inv_lref … Hl2) -Hl2 * #K0 #V0 [| #l0 ] #HK0 #HV0 [| #H1 ] +| #G #L2 #K2 #X #Y #Y0 #U #i #l2 #HLK2 #HXY0 #_ #HYU #IHXY #l1 #Hl21 #Hl1 #L1 #HL12 + elim (da_inv_lref … Hl1) -Hl1 * #K0 #V0 [| #l0 ] #HK0 #HV0 [| #H1 ] lapply (drop_mono … HK0 … HLK2) -HK0 #H2 destruct - lapply (le_plus_to_le_r … Hl12) -Hl12 #Hl12 + lapply (le_plus_to_le_r … Hl21) -Hl21 #Hl21 elim (lsubsv_drop_O1_trans … HL12 … HLK2) -L2 #X #H #HLK1 elim (lsubsv_inv_pair2 … H) -H * #K1 [ #HK12 #H destruct lapply (lsubsv_fwd_lsubd … HK12) #H lapply (lsubd_da_trans … HV0 … H) -H #H elim (da_inv_sta … H) -H - elim (IHXY … Hl12 HV0 … HK12) -K2 -Hl12 #Y1 + elim (IHXY … Hl21 HV0 … HK12) -K2 -Hl21 #Y1 lapply (drop_fwd_drop2 … HLK1) elim (lift_total Y1 0 (i+1)) /3 width=12 by lstas_ldec, cpcs_lift, ex2_intro/ - | #V #l #_ #_ #HVX #_ #HV #HX #HK12 #_ #H destruct - lapply (da_mono … HX … HV0) -HX #H destruct - elim (IHXY … Hl12 HV0 … HK12) -K2 #Y0 #HXY0 #HY0 + | #V #l1 #HXV #_ #HV #HX #HK12 #_ #H destruct + lapply (da_mono … HV0 … HX) -HX #H destruct + elim (hsnv_inv_cast … HXV) -HXV #_ #_ #H + lapply (H … Hl21) -H #HXV + elim (IHXY … Hl21 HV0 … HK12) -K2 -Hl21 #Y0 #HXY0 #HY0 elim (da_inv_sta … HV) -HV #W #HVW - elim (lstas_total … HVW (l1+1)) -W #W #HVW - lapply (HVX … Hl12 HVW HXY0) -HVX -Hl12 -HXY0 #HWY0 - lapply (cpcs_trans … HWY0 … HY0) -Y0 - lapply (drop_fwd_drop2 … HLK1) + elim (lstas_total … HVW (l2+1)) -W #W #HVW + lapply (cpes_inv_lstas_eq … HXV … HXY0 … HVW) -HXV -HXY0 #HY0W + lapply (cpcs_canc_sn … HY0W … HY0) -Y0 #HYW elim (lift_total W 0 (i+1)) - /4 width=12 by lstas_ldef, lstas_cast, cpcs_lift, ex2_intro/ + lapply (drop_fwd_drop2 … HLK1) + /4 width=12 by cpcs_lift, lstas_cast, lstas_ldef, ex2_intro/ ] | #a #I #G #L2 #V2 #T2 #U2 #l1 #_ #IHTU2 #l2 #Hl12 #Hl2 #L1 #HL12 lapply (da_inv_bind … Hl2) -Hl2 #Hl2