From a041f17ec3bee5a321e6feee9937229e93c39a72 Mon Sep 17 00:00:00 2001 From: Ferruccio Guidi Date: Mon, 26 Sep 2016 20:39:02 +0000 Subject: [PATCH] - reconstruction of lfpx_frees.ma begins ... - minor improvements --- .../basic_2/relocation/lexs_lexs.ma | 4 +- .../basic_2/rt_transition/lfpx_frees.ma | 146 +++++++++--------- .../lambdadelta/basic_2/static/frees_fqup.ma | 57 +++++++ .../lfxs_main.etc => static/lfxs_main.ma} | 22 ++- .../ground_2/relocation/rtmap_sor.ma | 7 + 5 files changed, 164 insertions(+), 72 deletions(-) rename matita/matita/contribs/lambdadelta/basic_2/{etc_new/lfxs_main.etc => static/lfxs_main.ma} (62%) diff --git a/matita/matita/contribs/lambdadelta/basic_2/relocation/lexs_lexs.ma b/matita/matita/contribs/lambdadelta/basic_2/relocation/lexs_lexs.ma index 91dc22297..13ec6ca81 100644 --- a/matita/matita/contribs/lambdadelta/basic_2/relocation/lexs_lexs.ma +++ b/matita/matita/contribs/lambdadelta/basic_2/relocation/lexs_lexs.ma @@ -45,8 +45,8 @@ theorem lexs_trans (RN) (RP) (f): lexs_transitive RN RN RN RN RP → (* Basic_2A1: includes: lpx_sn_conf *) theorem lexs_conf (RN1) (RP1) (RN2) (RP2): ∀L,f. - (∀g,I,K,V,n. ⬇*[n] L ≡ K.ⓑ{I}V → ⫱*[n] f = ⫯g → lexs_pw_confluent2_R RN1 RN2 RN1 RP1 RN2 RP2 g K V) → - (∀g,I,K,V,n. ⬇*[n] L ≡ K.ⓑ{I}V → ⫱*[n] f = ↑g → lexs_pw_confluent2_R RP1 RP2 RN1 RP1 RN2 RP2 g K V) → + (∀g,I,K,V,n. ⬇*[n] L ≡ K.ⓑ{I}V → ⫯g = ⫱*[n] f → lexs_pw_confluent2_R RN1 RN2 RN1 RP1 RN2 RP2 g K V) → + (∀g,I,K,V,n. ⬇*[n] L ≡ K.ⓑ{I}V → ↑g = ⫱*[n] f → lexs_pw_confluent2_R RP1 RP2 RN1 RP1 RN2 RP2 g K V) → pw_confluent2 … (lexs RN1 RP1 f) (lexs RN2 RP2 f) L. #RN1 #RP1 #RN2 #RP2 #L elim L -L [ #f #_ #_ #L1 #H1 #L2 #H2 >(lexs_inv_atom1 … H1) >(lexs_inv_atom1 … H2) -H2 -H1 diff --git a/matita/matita/contribs/lambdadelta/basic_2/rt_transition/lfpx_frees.ma b/matita/matita/contribs/lambdadelta/basic_2/rt_transition/lfpx_frees.ma index d9f6445a0..47d35f2e5 100644 --- a/matita/matita/contribs/lambdadelta/basic_2/rt_transition/lfpx_frees.ma +++ b/matita/matita/contribs/lambdadelta/basic_2/rt_transition/lfpx_frees.ma @@ -15,87 +15,95 @@ include "basic_2/multiple/frees_lreq.ma". include "basic_2/multiple/frees_lift.ma". *) +include "basic_2/relocation/drops_lexs.ma". include "basic_2/s_computation/fqup_weight.ma". +include "basic_2/static/frees_drops.ma". include "basic_2/rt_transition/cpx_drops.ma". -include "basic_2/rt_transition/lfpx.ma". (* UNCOUNTED PARALLEL RT-TRANSITION FOR LOCAL ENV.S ON REFERRED ENTRIES *****) -(* Properties with context-sensitive free variables ***************************) +(* Properties with context-sensitive free variables *************************) -lemma lpx_cpx_frees_fwd_sge: ∀h,G,L1,U1,U2. ⦃G, L1⦄ ⊢ U1 ⬈[h] U2 → - ∀L2. ⦃G, L1⦄ ⊢ ⬈[h, U1] L2 → - ∀g1. L1 ⊢ 𝐅*⦃U1⦄ ≡ g1 → ∀g2. L2 ⊢ 𝐅*⦃U2⦄ ≡ g2 → - g2 ⊆ g1. -#h #G #L1 #U1 @(fqup_wf_ind_eq … G L1 U1) -G -L1 -U1 -#G0 #L0 #U0 #IH #G #L1 * * -[ #s #HG #HL #HU #U2 #H0 #L2 #_ #g1 #H1 #g2 #H2 -IH -G0 -L0 -U0 - elim (cpx_inv_sort1 … H0) -H0 #H destruct - /3 width=3 by frees_inv_sort, sle_isid_sn/ -| #i #HG #HL #HU #U2 #H0 #L2 #HL12 #g1 #H1 #g2 #H2 destruct - elim (cpx_inv_lref1_drops … H0) -H0 - [ #H destruct - lapply (frees_inv_lref … H1) -H1 #Hg1 - lapply (frees_inv_sort … H2) -H2 #Hg2 /2 width=1 by sle_isid_sn/ +axiom pippo: ∀RN,RP,L1,i. ⬇*[Ⓕ, 𝐔❴i❵] L1 ≡ ⋆ → + ∀f,L2. L1 ⦻*[RN, RP, f] L2 → + ⬇*[Ⓕ, 𝐔❴i❵] L2 ≡ ⋆. +(* +#RN #RP #L1 #i #H1 #f #L2 #H2 +lapply (lexs_co_dropable_sn … H1 … H2) // -HL1 -H2 +*) +lemma coafter_uni_sn: ∀i,f. 𝐔❴i❵ ~⊚ f ≡ ↑*[i] f. +#i elim i -i /2 width=5 by coafter_isid_sn, coafter_next/ +qed. +lemma sle_pushs: ∀f1,f2. f1 ⊆ f2 → ∀i. ↑*[i] f1 ⊆ ↑*[i] f2. +#f1 #f2 #Hf12 #i elim i -i /2 width=5 by sle_push/ +qed. -| #l #HG #HL #HU #U2 #H0 #L2 #_ #g1 #H1 #g2 #H2 -IH -G0 -L0 -U0 - lapply (cpx_inv_gref1 … H0) -H0 #H destruct - /3 width=3 by frees_inv_gref, sle_isid_sn/ - -| #j #HG #HL #HU #U2 #H1 #L2 #HL12 #i #H2 elim (cpx_inv_lref1 … H1) -H1 - [ #H destruct elim (frees_inv_lref … H2) -H2 // - * #I #K2 #W2 #Hj #Hji #HLK2 #HW2 - elim (lpx_drop_trans_O1 … HL12 … HLK2) -HL12 #Y #HLK1 #H - elim (lpx_inv_pair2 … H) -H #K1 #W1 #HK12 #HW12 #H destruct - /4 width=11 by frees_lref_be, fqup_lref/ - | * #I #K1 #W1 #W0 #HLK1 #HW10 #HW0U2 - lapply (drop_fwd_drop2 … HLK1) #H0 - elim (lpx_drop_conf … H0 … HL12) -H0 -HL12 #K2 #HK12 #HLK2 - elim (ylt_split i (j+1)) >yplus_SO2 #Hji - [ -IH elim (frees_inv_lift_be … H2 … HLK2 … HW0U2) /2 width=1 by ylt_fwd_succ2/ - | lapply (frees_inv_lift_ge … H2 … HLK2 … HW0U2 ?) -L2 -U2 // destruct - /4 width=11 by frees_lref_be, fqup_lref, yle_succ1_inj/ - ] - ] -| -IH #p #HG #HL #HU #U2 #H1 >(cpx_inv_gref1 … H1) -H1 destruct - #L2 #_ #i #H2 elim (frees_inv_gref … H2) -| #a #I #W1 #U1 #HG #HL #HU #X #HX #L2 #HL12 #i #Hi destruct - elim (cpx_inv_bind1 … HX) -HX * - [ #W2 #U2 #HW12 #HU12 #H destruct - elim (frees_inv_bind_O … Hi) -Hi - /4 width=7 by frees_bind_dx_O, frees_bind_sn, lpx_pair/ - | #U2 #HU12 #HXU2 #H1 #H2 destruct - lapply (frees_lift_ge … Hi (L2.ⓓW1) (Ⓕ) … HXU2 ?) - /4 width=7 by frees_bind_dx_O, lpx_pair, drop_drop/ - ] -| #I #W1 #X1 #HG #HL #HU #X2 #HX2 #L2 #HL12 #i #Hi destruct - elim (cpx_inv_flat1 … HX2) -HX2 * - [ #W2 #U2 #HW12 #HU12 #H destruct - elim (frees_inv_flat … Hi) -Hi /3 width=7 by frees_flat_dx, frees_flat_sn/ - | #HU12 #H destruct /3 width=7 by frees_flat_dx/ - | #HW12 #H destruct /3 width=7 by frees_flat_sn/ - | #b #W2 #V1 #V2 #U1 #U2 #HW12 #HV12 #HU12 #H1 #H2 #H3 destruct - elim (frees_inv_bind … Hi) -Hi #Hi - [ elim (frees_inv_flat … Hi) -Hi - /4 width=7 by frees_flat_dx, frees_flat_sn, frees_bind_sn/ - | lapply (lreq_frees_trans … Hi (L2.ⓛV2) ?) /2 width=1 by lreq_succ/ -Hi #HU2 - lapply (frees_weak … HU2 0 ?) -HU2 - /5 width=7 by frees_bind_dx_O, frees_flat_dx, lpx_pair/ +axiom monotonic_sle_sor: ∀f1,g1. f1 ⊆ g1 → ∀f2,g2. f2 ⊆ g2 → + ∀f. f1 ⋓ f2 ≡ f → ∀g. g1 ⋓ g2 ≡ g → f ⊆ g. + +axiom sle_tl: ∀f1,f2. f1 ⊆ f2 → ⫱f1 ⊆ ⫱f2. + +axiom frees_inv_lifts_SO: ∀b,f,L,U. L ⊢ 𝐅*⦃U⦄ ≡ f → + ∀K. ⬇*[b, 𝐔❴1❵] L ≡ K → ∀T. ⬆*[1] T ≡ U → + K ⊢ 𝐅*⦃T⦄ ≡ ⫱f. + +(* Basic_2A1: was: lpx_cpx_frees_trans *) +lemma cpx_frees_trans_lexs: ∀h,G,L1,T1,f1. L1 ⊢ 𝐅*⦃T1⦄ ≡ f1 → + ∀L2. L1 ⦻*[cpx h G, cfull, f1] L2 → + ∀T2. ⦃G, L1⦄ ⊢ T1 ⬈[h] T2 → + ∃∃f2. L2 ⊢ 𝐅*⦃T2⦄ ≡ f2 & f2 ⊆ f1. +#h #G #L1 #T1 @(fqup_wf_ind_eq … G L1 T1) -G -L1 -T1 +#G0 #L0 #U0 #IH #G #L1 * * +[ -IH #s #HG #HL #HU #g1 #H1 #L2 #_ #U2 #H0 destruct + lapply (frees_inv_sort … H1) -H1 #Hg1 + elim (cpx_inv_sort1 … H0) -H0 #H destruct + /3 width=3 by frees_sort_gen, sle_refl, ex2_intro/ +| #i #HG #HL #HU #g1 #H1 #L2 #H2 #U2 #H0 destruct + elim (frees_inv_lref_drops … H1) -H1 * + [ -IH #HL1 #Hg1 + elim (cpx_inv_lref1_drops … H0) -H0 + [ #H destruct lapply (pippo … HL1 … H2) -HL1 -H2 + /3 width=3 by frees_lref_atom, sle_refl, ex2_intro/ + | * -H2 -Hg1 #I #K1 #V1 #V2 #HLK1 + lapply (drops_TF … HLK1) -HLK1 #HLK1 + lapply (drops_mono … HLK1 … HL1) -L1 #H destruct ] - | #b #W2 #W0 #V1 #V2 #U1 #U2 #HW12 #HW20 #HV12 #HU12 #H1 #H2 #H3 destruct - elim (frees_inv_bind_O … Hi) -Hi #Hi - [ /4 width=7 by frees_flat_dx, frees_bind_sn/ - | elim (frees_inv_flat … Hi) -Hi - [ #HW0 lapply (frees_inv_lift_ge … HW0 L2 (Ⓕ) … HW20 ?) -W0 - /3 width=7 by frees_flat_sn, drop_drop/ - | /5 width=7 by frees_bind_dx_O, frees_flat_dx, lpx_pair/ - ] + | #f1 #I #K1 #V1 #Hf1 #HLK1 #H destruct + elim (cpx_inv_lref1_drops … H0) -H0 + [ #H destruct + elim (lexs_drops_conf_next … H2 … HLK1) -H2 [ |*: // ] #K2 #V2 #HLK2 #HK12 #HV12 + elim (IH … Hf1 … HK12 … HV12) /2 width=2 by fqup_lref/ -L1 -K1 -V1 #f2 #Hf2 #Hf21 + /4 width=7 by frees_lref_pushs, frees_lref_pair, drops_refl, sle_next, ex2_intro, sle_pushs/ + | * #J #Y #X #V2 #H #HV12 #HVU2 + lapply (drops_mono … H … HLK1) -H #H destruct + elim (lexs_drops_conf_next … H2 … HLK1) -H2 [ |*: // ] #K2 #V0 #HLK2 #HK12 #_ + lapply (drops_isuni_fwd_drop2 … HLK2) // -V0 #HLK2 + elim (IH … Hf1 … HK12 … HV12) /2 width=2 by fqup_lref/ -I -L1 -K1 -V1 #f2 #Hf2 #Hf21 + lapply (frees_lifts … Hf2 … HLK2 … HVU2 ??) /4 width=7 by sle_weak, ex2_intro, sle_pushs/ ] ] -] -qed-. +| -IH #l #HG #HL #HU #g1 #H1 #L2 #_ #U2 #H0 destruct + lapply (frees_inv_gref … H1) -H1 #Hg1 + lapply (cpx_inv_gref1 … H0) -H0 #H destruct + /3 width=3 by frees_gref_gen, sle_refl, ex2_intro/ +| #p #I #V1 #T1 #HG #HL #HU #g1 #H1 #L2 #H2 #U2 #H0 destruct + elim (frees_inv_bind … H1) -H1 #gV1 #gT1 #HgV1 #HgT1 #Hg1 + elim (cpx_inv_bind1 … H0) -H0 * + [ #V2 #T2 #HV12 #HT12 #H destruct + lapply (sle_lexs_trans … H2 gV1 ?) /2 width=2 by sor_inv_sle_sn/ #HL12V + lapply (sle_lexs_trans … H2 (⫱gT1) ?) /2 width=2 by sor_inv_sle_dx/ -H2 #HL12T + lapply (lexs_inv_tl … I … HL12T … HV12 ?) // -HL12T #HL12T + elim (IH … HgV1 … HL12V … HV12) // -HgV1 -HL12V -HV12 #gV2 #HgV2 #HgV21 + elim (IH … HgT1 … HL12T … HT12) // -IH -HgT1 -HL12T -HT12 #gT2 #HgT2 #HgT21 + elim (sor_isfin_ex gV2 (⫱gT2)) /3 width=3 by frees_fwd_isfin, isfin_tl/ + /4 width=10 by frees_bind, monotonic_sle_sor, sle_tl, ex2_intro/ + | #T2 #HT12 #HUT2 #H0 #H1 destruct -HgV1 + lapply (sle_lexs_trans … H2 (⫱gT1) ?) /2 width=2 by sor_inv_sle_dx/ -H2 #HL12T + lapply (lexs_inv_tl … Abbr … V1 V1 HL12T ??) // -HL12T #HL12T + elim (IH … HgT1 … HL12T … HT12) // -IH -HgT1 -HL12T -HT12 #gT2 #HgT2 #HgT21 + lapply (frees_inv_lifts_SO (Ⓣ) … HgT2 … L2 … HUT2) [ /3 width=1 by drops_refl, drops_drop/ ] lemma cpx_frees_trans: ∀h,o,G. frees_trans (cpx h o G). /2 width=8 by lpx_cpx_frees_trans/ qed-. diff --git a/matita/matita/contribs/lambdadelta/basic_2/static/frees_fqup.ma b/matita/matita/contribs/lambdadelta/basic_2/static/frees_fqup.ma index c82690309..d89aaaaae 100644 --- a/matita/matita/contribs/lambdadelta/basic_2/static/frees_fqup.ma +++ b/matita/matita/contribs/lambdadelta/basic_2/static/frees_fqup.ma @@ -12,6 +12,7 @@ (* *) (**************************************************************************) +include "basic_2/relocation/drops.ma". include "basic_2/s_computation/fqup_weight.ma". include "basic_2/static/frees.ma". @@ -44,3 +45,59 @@ lemma frees_total: ∀L,T. ∃f. L ⊢ 𝐅*⦃T⦄ ≡ f. ] ] qed-. + +(* Properties with plus-iterated supclosure *********************************) + +lemma frees_drops_next: ∀f1,L1,T1. L1 ⊢ 𝐅*⦃T1⦄ ≡ f1 → + ∀I2,L2,V2,n. ⬇*[n] L1 ≡ L2.ⓑ{I2}V2 → + ∀g1. ⫯g1 = ⫱*[n] f1 → + ∃∃g2. L2 ⊢ 𝐅*⦃V2⦄ ≡ g2 & g2 ⊆ g1. +#f1 #L1 #T1 #H elim H -f1 -L1 -T1 +[ #f1 #I1 #Hf1 #I2 #L2 #V2 #n #HL12 + elim (drops_inv_atom1 … HL12) -HL12 #H destruct +| #f1 #I1 #L1 #V1 #s #_ #IH #I2 #L2 #V2 * + [ -IH #_ #g1 #Hgf1 elim (discr_next_push … Hgf1) + | #n #HL12 lapply (drops_inv_drop1 … HL12) -HL12 + #HL12 #g1 (injective_next … Hgf1) -g1 + /2 width=3 by sle_refl, ex2_intro/ + | -Hf1 #n #HL12 lapply (drops_inv_drop1 … HL12) -HL12 + #HL12 #g1 tls_xn #H2 elim (IHT1 … H2) -IHT1 -H2 + /3 width=6 by drops_drop, sor_sle_dx, ex2_intro/ + ] +| #fV1 #fT1 #f1 #I1 #L1 #V1 #T1 #_ #_ #Hf1 #IHV1 #IHT1 #I2 #L2 #V2 #n #HL12 #g1 #Hgf1 + lapply (sor_tls … Hf1 n) -Hf1