From: Ferruccio Guidi Date: Wed, 1 Aug 2018 18:47:17 +0000 (+0200) Subject: update in ground_2 and basic_2 X-Git-Tag: make_still_working~291 X-Git-Url: http://matita.cs.unibo.it/gitweb/?p=helm.git;a=commitdiff_plain;h=ede00573e3e4cb28df7ca9a5dae6228c2b432608 update in ground_2 and basic_2 + cnv_cpm_conf_lpr_aux (rt-validity implies diamond property) + one addition in the arithmetics library --- diff --git a/matita/matita/contribs/lambdadelta/basic_2/dynamic/cnv.ma b/matita/matita/contribs/lambdadelta/basic_2/dynamic/cnv.ma index 398ef6783..97c1feca2 100644 --- a/matita/matita/contribs/lambdadelta/basic_2/dynamic/cnv.ma +++ b/matita/matita/contribs/lambdadelta/basic_2/dynamic/cnv.ma @@ -139,3 +139,8 @@ lemma cnv_inv_cast (a) (h): ∀G,L,U,T. ⦃G, L⦄ ⊢ ⓝU.T ![a, h] → ∃∃U0. ⦃G, L⦄ ⊢ U ![a, h] & ⦃G, L⦄ ⊢ T ![a, h] & ⦃G, L⦄ ⊢ U ➡*[h] U0 & ⦃G, L⦄ ⊢ T ➡*[1, h] U0. /2 width=3 by cnv_inv_cast_aux/ qed-. + +(* Basic_2A1: removed theorems 6: + snv_fwd_da snv_fwd_lstas snv_cast_scpes + shnv_cast shnv_inv_cast snv_shnv_cast +*) diff --git a/matita/matita/contribs/lambdadelta/basic_2/dynamic/cnv_cpm_conf.ma b/matita/matita/contribs/lambdadelta/basic_2/dynamic/cnv_cpm_conf.ma new file mode 100644 index 000000000..160d23f88 --- /dev/null +++ b/matita/matita/contribs/lambdadelta/basic_2/dynamic/cnv_cpm_conf.ma @@ -0,0 +1,489 @@ +(**************************************************************************) +(* ___ *) +(* ||M|| *) +(* ||A|| A project by Andrea Asperti *) +(* ||T|| *) +(* ||I|| Developers: *) +(* ||T|| The HELM team. *) +(* ||A|| http://helm.cs.unibo.it *) +(* \ / *) +(* \ / This file is distributed under the terms of the *) +(* v GNU General Public License Version 2 *) +(* *) +(**************************************************************************) + +include "basic_2/rt_transition/lpr_lpr.ma". +include "basic_2/rt_computation/cpms_lsubr.ma". +include "basic_2/rt_computation/cpms_fpbg.ma". +include "basic_2/rt_computation/cpms_cpms.ma". +include "basic_2/dynamic/cnv_drops.ma". +include "basic_2/dynamic/cnv_preserve_far.ma". + +(* CONTEXT-SENSITIVE NATIVE VALIDITY FOR TERMS ******************************) + +(* Far diamond propery with t-bound rt-transition for terms *****************) + +fact cnv_cpm_conf_lpr_atom_atom_aux (h) (G) (L1) (L2) (I): + ∃∃T. ⦃G,L1⦄ ⊢ ⓪{I} ➡*[0,h] T & ⦃G, L2⦄ ⊢ ⓪{I} ➡*[O,h] T. +/2 width=3 by ex2_intro/ qed-. + +fact cnv_cpm_conf_lpr_atom_ess_aux (h) (G) (L1) (L2) (s): + ∃∃T. ⦃G,L1⦄ ⊢ ⋆s ➡*[1,h] T & ⦃G,L2⦄ ⊢ ⋆(next h s) ➡*[h] T. +/3 width=3 by cpm_cpms, ex2_intro/ qed-. + +fact cnv_cpm_conf_lpr_atom_delta_aux (a) (h) (o) (G) (L) (i): + (∀G0,L0,T0. ⦃G,L,#i⦄ >[h,o] ⦃G0,L0,T0⦄ → IH_cnv_cpms_conf_lpr a h G0 L0 T0) → + ⦃G,L⦄⊢#i![a,h] → + ∀K,V. ⬇*[i]L ≘ K.ⓓV → + ∀n,XV. ⦃G,K⦄ ⊢ V ➡[n,h] XV → + ∀X. ⬆*[↑i]XV ≘ X → + ∀L1. ⦃G,L⦄ ⊢ ➡[h] L1 → ∀L2. ⦃G,L⦄ ⊢ ➡[h] L2 → + ∃∃T. ⦃G,L1⦄ ⊢ #i ➡*[n,h] T & ⦃G,L2⦄ ⊢ X ➡*[h] T. +#a #h #o #G #L #i #IH #HT #K #V #HLK #n #XV #HVX #X #HXV #L1 #HL1 #L2 #HL2 +lapply (cnv_lref_fwd_drops … HT … HLK) -HT #HV +elim (lpr_drops_conf … HLK … HL1) -HL1 // #Y1 #H1 #HLK1 +elim (lpr_inv_pair_sn … H1) -H1 #K1 #V1 #HK1 #HV1 #H destruct +elim (lpr_drops_conf … HLK … HL2) -HL2 // #Y2 #H2 #HLK2 +elim (lpr_inv_pair_sn … H2) -H2 #K2 #V2 #HK2 #_ #H destruct +lapply (drops_isuni_fwd_drop2 … HLK2) -V2 // #HLK2 +lapply (fqup_lref (Ⓣ) … G … HLK) -HLK #HLK +elim (cnv_cpm_conf_lpr_far … IH … HV1 … HVX … HK1 … HK2) [|*: /2 width=1 by fqup_fpbg/ ] -L -K -V +[h,o] ⦃G0,L0,T0⦄ → IH_cnv_cpms_conf_lpr a h G0 L0 T0) → + ⦃G,L⦄⊢#i![a,h] → + ∀K,W. ⬇*[i]L ≘ K.ⓛW → + ∀n,XW. ⦃G,K⦄ ⊢ W ➡[n,h] XW → + ∀X. ⬆*[↑i]XW ≘ X → + ∀L1. ⦃G,L⦄ ⊢ ➡[h] L1 → ∀L2. ⦃G,L⦄ ⊢ ➡[h] L2 → + ∃∃T. ⦃G,L1⦄ ⊢ #i ➡*[↑n,h] T & ⦃G,L2⦄ ⊢ X ➡*[h] T. +#a #h #o #G #L #i #IH #HT #K #W #HLK #n #XW #HWX #X #HXW #L1 #HL1 #L2 #HL2 +lapply (cnv_lref_fwd_drops … HT … HLK) -HT #HW +elim (lpr_drops_conf … HLK … HL1) -HL1 // #Y1 #H1 #HLK1 +elim (lpr_inv_pair_sn … H1) -H1 #K1 #W1 #HK1 #HW1 #H destruct +elim (lpr_drops_conf … HLK … HL2) -HL2 // #Y2 #H2 #HLK2 +elim (lpr_inv_pair_sn … H2) -H2 #K2 #W2 #HK2 #_ #H destruct +lapply (drops_isuni_fwd_drop2 … HLK2) -W2 // #HLK2 +lapply (fqup_lref (Ⓣ) … G … HLK) -HLK #HLK +elim (cnv_cpm_conf_lpr_far … IH … HW1 … HWX … HK1 … HK2) [|*: /2 width=1 by fqup_fpbg/ ] -L -K -W +[h,o] ⦃G0,L0,T0⦄ → IH_cnv_cpms_conf_lpr a h G0 L0 T0) → + ⦃G,L⦄⊢#i![a,h] → + ∀K1,V1. ⬇*[i]L ≘ K1.ⓑ{I}V1 → ∀K2,V2. ⬇*[i]L ≘ K2.ⓑ{I}V2 → + ∀n1,XV1. ⦃G,K1⦄ ⊢ V1 ➡[n1,h] XV1 → ∀n2,XV2. ⦃G,K2⦄ ⊢ V2 ➡[n2,h] XV2 → + ∀X1. ⬆*[↑i]XV1 ≘ X1 → ∀X2. ⬆*[↑i]XV2 ≘ X2 → + ∀L1. ⦃G,L⦄ ⊢ ➡[h] L1 → ∀L2. ⦃G,L⦄ ⊢ ➡[h] L2 → + ∃∃T. ⦃G,L1⦄ ⊢ X1 ➡*[n2-n1,h] T & ⦃G,L2⦄ ⊢ X2 ➡*[n1-n2,h] T. +#a #h #o #I #G #L #i #IH #HT +#K #V #HLK #Y #X #HLY #n1 #XV1 #HVX1 #n2 #XV2 #HVX2 #X1 #HXV1 #X2 #HXV2 +#L1 #HL1 #L2 #HL2 +lapply (drops_mono … HLY … HLK) -HLY #H destruct +lapply (cnv_lref_fwd_drops … HT … HLK) -HT #HV +elim (lpr_drops_conf … HLK … HL1) -HL1 // #Y1 #H1 #HLK1 +elim (lpr_inv_pair_sn … H1) -H1 #K1 #V1 #HK1 #_ #H destruct +lapply (drops_isuni_fwd_drop2 … HLK1) -V1 // #HLK1 +elim (lpr_drops_conf … HLK … HL2) -HL2 // #Y2 #H2 #HLK2 +elim (lpr_inv_pair_sn … H2) -H2 #K2 #V2 #HK2 #_ #H destruct +lapply (drops_isuni_fwd_drop2 … HLK2) -V2 // #HLK2 +lapply (fqup_lref (Ⓣ) … G … HLK) -HLK #HLK +elim (cnv_cpm_conf_lpr_far … IH … HVX1 … HVX2 … HK1 … HK2) [|*: /2 width=1 by fqup_fpbg/ ] -L -K -V +#V #HVX1 #HVX2 +elim (cpms_lifts_sn … HVX1 … HLK1 … HXV1) -XV1 -HLK1 #W1 #HVW1 #HXW1 +/3 width=11 by cpms_lifts_bi, ex2_intro/ +qed-. + +fact cnv_cpm_conf_lpr_delta_ell_aux (L) (K1) (K2) (V) (W) (i): + ⬇*[i]L ≘ K1.ⓓV → ⬇*[i]L ≘ K2.ⓛW → ⊥. +#L #K1 #K2 #V #W #i #HLK1 #HLK2 +lapply (drops_mono … HLK2 … HLK1) -L -i #H destruct +qed-. + +fact cnv_cpm_conf_lpr_bind_bind_aux (a) (h) (o) (p) (I) (G) (L) (V) (T): + (∀G0,L0,T0. ⦃G,L,ⓑ{p,I}V.T⦄ >[h,o] ⦃G0,L0,T0⦄ → IH_cnv_cpms_conf_lpr a h G0 L0 T0) → + ⦃G,L⦄ ⊢ ⓑ{p,I}V.T ![a,h] → + ∀V1. ⦃G,L⦄ ⊢ V ➡[h] V1 → ∀V2. ⦃G,L⦄ ⊢ V ➡[h] V2 → + ∀n1,T1. ⦃G,L.ⓑ{I}V⦄ ⊢ T ➡[n1,h] T1 → ∀n2,T2. ⦃G,L.ⓑ{I}V⦄ ⊢ T ➡[n2,h] T2 → + ∀L1. ⦃G,L⦄ ⊢ ➡[h] L1 → ∀L2. ⦃G,L⦄ ⊢ ➡[h] L2 → + ∃∃T. ⦃G,L1⦄ ⊢ ⓑ{p,I}V1.T1 ➡*[n2-n1,h] T & ⦃G,L2⦄ ⊢ ⓑ{p,I}V2.T2 ➡*[n1-n2,h] T. +#a #h #o #p #I #G0 #L0 #V0 #T0 #IH #H0 +#V1 #HV01 #V2 #HV02 #n1 #T1 #HT01 #n2 #T2 #HT02 +#L1 #HL01 #L2 #HL02 +elim (cnv_inv_bind … H0) -H0 #HV0 #HT0 +elim (cpr_conf_lpr … HV01 … HV02 … HL01 … HL02) #V #HV1 #HV2 +elim (cnv_cpm_conf_lpr_far … IH … HT01 … HT02 (L1.ⓑ{I}V1) … (L2.ⓑ{I}V2)) [|*: /2 width=1 by fqup_fpbg, lpr_pair/ ] +#T #HT1 #HT2 -L0 -V0 -T0 +/3 width=5 by cpms_bind_dx, ex2_intro/ +qed-. + +fact cnv_cpm_conf_lpr_bind_zeta_aux (a) (h) (o) (G) (L) (V) (T): + (∀G0,L0,T0. ⦃G,L,+ⓓV.T⦄ >[h,o] ⦃G0,L0,T0⦄ → IH_cnv_cpms_conf_lpr a h G0 L0 T0) → + ⦃G,L⦄ ⊢ +ⓓV.T ![a,h] → + ∀V1. ⦃G,L⦄ ⊢V ➡[h] V1 → + ∀n1,T1. ⦃G,L.ⓓV⦄ ⊢ T ➡[n1,h] T1 → ∀n2,T2. ⦃G,L.ⓓV⦄ ⊢ T ➡[n2,h] T2 → + ∀XT2. ⬆*[1]XT2 ≘ T2 → + ∀L1. ⦃G,L⦄ ⊢ ➡[h] L1 → ∀L2. ⦃G,L⦄ ⊢ ➡[h] L2 → + ∃∃T. ⦃G,L1⦄ ⊢ +ⓓV1.T1 ➡*[n2-n1,h] T & ⦃G,L2⦄ ⊢ XT2 ➡*[n1-n2,h] T. +#a #h #o #G0 #L0 #V0 #T0 #IH #H0 +#V1 #HV01 #n1 #T1 #HT01 #n2 #T2 #HT02 #XT2 #HXT2 +#L1 #HL01 #L2 #HL02 +elim (cnv_inv_bind … H0) -H0 #_ #HT0 +elim (cnv_cpm_conf_lpr_far … IH … HT01 … HT02 (L1.ⓓV1) … (L2.ⓓV1)) [|*: /2 width=1 by fqup_fpbg, lpr_pair/ ] -L0 -T0 -V0 +#T #HT1 #HT2 +elim (cpms_inv_lifts_sn … HT2 (Ⓣ) … L2 … HXT2) -T2 [| /3 width=1 by drops_refl, drops_drop/ ] #XT #HXT #HXT2 +/3 width=3 by cpms_zeta, ex2_intro/ +qed-. + +fact cnv_cpm_conf_lpr_zeta_zeta_aux (a) (h) (o) (G) (L) (V) (T): + (∀G0,L0,T0. ⦃G,L,+ⓓV.T⦄ >[h,o] ⦃G0,L0,T0⦄ → IH_cnv_cpms_conf_lpr a h G0 L0 T0) → + ⦃G,L⦄ ⊢ +ⓓV.T ![a,h] → + ∀n1,T1. ⦃G,L.ⓓV⦄ ⊢ T ➡[n1,h] T1 → ∀n2,T2. ⦃G,L.ⓓV⦄ ⊢ T ➡[n2,h] T2 → + ∀XT1. ⬆*[1]XT1 ≘ T1 → ∀XT2. ⬆*[1]XT2 ≘ T2 → + ∀L1. ⦃G,L⦄ ⊢ ➡[h] L1 → ∀L2. ⦃G,L⦄ ⊢ ➡[h] L2 → + ∃∃T. ⦃G,L1⦄ ⊢ XT1 ➡*[n2-n1,h] T & ⦃G,L2⦄ ⊢ XT2 ➡*[n1-n2,h] T. +#a #h #o #G0 #L0 #V0 #T0 #IH #H0 +#n1 #T1 #HT01 #n2 #T2 #HT02 #XT1 #HXT1 #XT2 #HXT2 +#L1 #HL01 #L2 #HL02 +elim (cnv_inv_bind … H0) -H0 #_ #HT0 +elim (cnv_cpm_conf_lpr_far … IH … HT01 … HT02 (L1.ⓓV0) … (L2.ⓓV0)) [|*: /2 width=1 by fqup_fpbg, lpr_pair/ ] -L0 -T0 +#T #HT1 #HT2 +elim (cpms_inv_lifts_sn … HT1 (Ⓣ) … L1 … HXT1) -T1 /3 width=2 by drops_refl, drops_drop/ #XT #HXT #HXT1 +elim (cpms_inv_lifts_sn … HT2 (Ⓣ) … L2 … HXT2) -T2 /3 width=2 by drops_refl, drops_drop/ #X #H #HXT2 +lapply (lifts_inj … H … HXT) -T #H destruct +/2 width=3 by ex2_intro/ +qed-. + +fact cnv_cpm_conf_lpr_appl_appl_aux (a) (h) (o) (G) (L) (V) (T): + (∀G0,L0,T0. ⦃G,L,ⓐV.T⦄ >[h,o] ⦃G0,L0,T0⦄ → IH_cnv_cpms_conf_lpr a h G0 L0 T0) → + ⦃G,L⦄ ⊢ ⓐV.T ![a,h] → + ∀V1. ⦃G,L⦄ ⊢ V ➡[h] V1 → ∀V2. ⦃G,L⦄ ⊢ V ➡[h] V2 → + ∀n1,T1. ⦃G,L⦄ ⊢ T ➡[n1,h] T1 → ∀n2,T2. ⦃G,L⦄ ⊢ T ➡[n2,h] T2 → + ∀L1. ⦃G,L⦄ ⊢ ➡[h] L1 → ∀L2. ⦃G,L⦄ ⊢ ➡[h] L2 → + ∃∃T. ⦃G,L1⦄ ⊢ ⓐV1.T1 ➡*[n2-n1,h] T & ⦃G,L2⦄ ⊢ ⓐV2.T2 ➡*[n1-n2,h] T. +#a #h #o #G0 #L0 #V0 #T0 #IH #H0 +#V1 #HV01 #V2 #HV02 #n1 #T1 #HT01 #n2 #T2 #HT02 +#L1 #HL01 #L2 #HL02 +elim (cnv_inv_appl … H0) -H0 #n0 #p0 #X01 #X02 #_ #HV0 #HT0 #_ #_ -n0 -p0 -X01 -X02 +elim (cpr_conf_lpr … HV01 … HV02 … HL01 … HL02) #V #HV1 #HV2 +elim (cnv_cpm_conf_lpr_far … IH … HT01 … HT02 … HL01 … HL02) [|*: /2 width=1 by fqup_fpbg/ ] +#T #HT1 #HT2 -L0 -V0 -T0 +/3 width=5 by cpms_appl_dx, ex2_intro/ +qed-. + +fact cnv_cpm_conf_lpr_appl_beta_aux (a) (h) (o) (p) (G) (L) (V) (W) (T): + (∀G0,L0,T0. ⦃G,L,ⓐV.ⓛ{p}W.T⦄ >[h,o] ⦃G0,L0,T0⦄ → IH_cnv_cpms_conf_lpr a h G0 L0 T0) → + ⦃G,L⦄ ⊢ ⓐV.ⓛ{p}W.T ![a,h] → + ∀V1. ⦃G,L⦄ ⊢ V ➡[h] V1 → ∀V2. ⦃G,L⦄ ⊢ V ➡[h] V2 → + ∀W2. ⦃G,L⦄ ⊢ W ➡[h] W2 → + ∀n1,T1. ⦃G,L⦄ ⊢ ⓛ{p}W.T ➡[n1,h] T1 → ∀n2,T2. ⦃G,L.ⓛW⦄ ⊢ T ➡[n2,h] T2 → + ∀L1. ⦃G,L⦄ ⊢ ➡[h] L1 → ∀L2. ⦃G,L⦄ ⊢ ➡[h] L2 → + ∃∃T. ⦃G,L1⦄ ⊢ ⓐV1.T1 ➡*[n2-n1,h] T & ⦃G,L2⦄ ⊢ ⓓ{p}ⓝW2.V2.T2 ➡*[n1-n2,h] T. +#a #h #o #p #G0 #L0 #V0 #W0 #T0 #IH #H0 +#V1 #HV01 #V2 #HV02 #W2 #HW02 #n1 #X #HX #n2 #T2 #HT02 +#L1 #HL01 #L2 #HL02 +elim (cnv_inv_appl … H0) -H0 #n0 #p0 #X01 #X02 #_ #HV0 #H0 #_ #_ -n0 -p0 -X01 -X02 +elim (cnv_inv_bind … H0) -H0 #HW0 #HT0 +elim (cpm_inv_abst1 … HX) -HX #W1 #T1 #HW01 #HT01 #H destruct +elim (cpr_conf_lpr … HV01 … HV02 … HL01 … HL02) #V #HV1 #HV2 +elim (cpr_conf_lpr … HW01 … HW02 … HL01 … HL02) #W #HW1 #HW2 +elim (cnv_cpm_conf_lpr_far … IH … HT01 … HT02 (L1.ⓛW1) … (L2.ⓛW2)) [|*: /2 width=1 by fqup_fpbg, lpr_pair/ ] +#T #HT1 #HT2 -L0 -V0 -W0 -T0 +lapply (lsubr_cpms_trans … HT2 (L2.ⓓⓝW2.V2) ?) -HT2 [ /2 width=1 by lsubr_beta/ ] #HT2 +/4 width=5 by cpms_beta_dx, cpms_bind_dx, cpm_cast, ex2_intro/ +qed-. + +fact cnv_cpm_conf_lpr_appl_theta_aux (a) (h) (o) (p) (G) (L) (V) (W) (T): + (∀G0,L0,T0. ⦃G,L,ⓐV.ⓓ{p}W.T⦄ >[h,o] ⦃G0,L0,T0⦄ → IH_cnv_cpms_conf_lpr a h G0 L0 T0) → + ⦃G,L⦄ ⊢ ⓐV.ⓓ{p}W.T ![a,h] → + ∀V1. ⦃G,L⦄ ⊢ V ➡[h] V1 → ∀V2. ⦃G,L⦄ ⊢ V ➡[h] V2 → + ∀W2. ⦃G,L⦄ ⊢ W ➡[h] W2 → + ∀n1,T1. ⦃G,L⦄ ⊢ ⓓ{p}W.T ➡[n1,h] T1 → ∀n2,T2. ⦃G,L.ⓓW⦄ ⊢ T ➡[n2,h] T2 → + ∀U2. ⬆*[1]V2 ≘ U2 → + ∀L1. ⦃G,L⦄ ⊢ ➡[h] L1 → ∀L2. ⦃G,L⦄ ⊢ ➡[h] L2 → + ∃∃T. ⦃G,L1⦄ ⊢ ⓐV1.T1 ➡*[n2-n1,h] T & ⦃G,L2⦄ ⊢ ⓓ{p}W2.ⓐU2.T2 ➡*[n1-n2,h] T. +#a #h #o #p #G0 #L0 #V0 #W0 #T0 #IH #H0 +#V1 #HV01 #V2 #HV02 #W2 #HW02 #n1 #X #HX #n2 #T2 #HT02 #U2 #HVU2 +#L1 #HL01 #L2 #HL02 +elim (cnv_inv_appl … H0) -H0 #n0 #p0 #X01 #X02 #_ #HV0 #H0 #_ #_ -n0 -p0 -X01 -X02 +elim (cnv_inv_bind … H0) -H0 #HW0 #HT0 +elim (cpr_conf_lpr … HV01 … HV02 … HL01 … HL02) #V #HV1 #HV2 +elim (cpm_lifts_sn … HV2 (Ⓣ) … (L2.ⓓW2) … HVU2) -HVU2 [| /3 width=1 by drops_refl, drops_drop/ ] #U #HVU #HU2 +elim (cpm_inv_abbr1 … HX) -HX * +[ #W1 #T1 #HW01 #HT01 #H destruct + elim (cpr_conf_lpr … HW01 … HW02 … HL01 … HL02) #W #HW1 #HW2 + elim (cnv_cpm_conf_lpr_far … IH … HT01 … HT02 (L1.ⓓW1) … (L2.ⓓW2)) [|*: /2 width=1 by fqup_fpbg, lpr_pair/ ] + #T #HT1 #HT2 -L0 -V0 -W0 -T0 + /4 width=7 by cpms_theta_dx, cpms_appl_dx, cpms_bind_dx, ex2_intro/ +| #T1 #HT01 #HX #H destruct + elim (cnv_cpm_conf_lpr_far … IH … HT01 … HT02 (L1.ⓓW2) … (L2.ⓓW2)) [|*: /2 width=1 by fqup_fpbg, lpr_pair/ ] + #T #HT1 #HT2 -L0 -V0 -W0 -T0 + elim (cpms_inv_lifts_sn … HT1 (Ⓣ) … L1 … HX) -T1 [| /3 width=1 by drops_refl, drops_drop/ ] #X0 #HXT #HX0 + /4 width=7 by cpms_zeta, cpms_appl_dx, lifts_flat, ex2_intro/ +] +qed-. + +fact cnv_cpm_conf_lpr_beta_beta_aux (a) (h) (o) (p) (G) (L) (V) (W) (T): + (∀G0,L0,T0. ⦃G,L,ⓐV.ⓛ{p}W.T⦄ >[h,o] ⦃G0,L0,T0⦄ → IH_cnv_cpms_conf_lpr a h G0 L0 T0) → + ⦃G,L⦄ ⊢ ⓐV.ⓛ{p}W.T ![a,h] → + ∀V1. ⦃G,L⦄ ⊢ V ➡[h] V1 → ∀V2. ⦃G,L⦄ ⊢ V ➡[h] V2 → + ∀W1. ⦃G,L⦄ ⊢ W ➡[h] W1 → ∀W2. ⦃G,L⦄ ⊢ W ➡[h] W2 → + ∀n1,T1. ⦃G,L.ⓛW⦄ ⊢ T ➡[n1,h] T1 → ∀n2,T2. ⦃G,L.ⓛW⦄ ⊢ T ➡[n2,h] T2 → + ∀L1. ⦃G,L⦄ ⊢ ➡[h] L1 → ∀L2. ⦃G,L⦄ ⊢ ➡[h] L2 → + ∃∃T. ⦃G,L1⦄ ⊢ ⓓ{p}ⓝW1.V1.T1 ➡*[n2-n1,h] T & ⦃G,L2⦄ ⊢ ⓓ{p}ⓝW2.V2.T2 ➡*[n1-n2,h] T. +#a #h #o #p #G0 #L0 #V0 #W0 #T0 #IH #H0 +#V1 #HV01 #V2 #HV02 #W1 #HW01 #W2 #HW02 #n1 #T1 #HT01 #n2 #T2 #HT02 +#L1 #HL01 #L2 #HL02 +elim (cnv_inv_appl … H0) -H0 #n0 #p0 #X01 #X02 #_ #HV0 #H0 #_ #_ -n0 -p0 -X01 -X02 +elim (cnv_inv_bind … H0) -H0 #HW0 #HT0 +elim (cpr_conf_lpr … HV01 … HV02 … HL01 … HL02) #V #HV1 #HV2 +elim (cpr_conf_lpr … HW01 … HW02 … HL01 … HL02) #W #HW1 #HW2 +elim (cnv_cpm_conf_lpr_far … IH … HT01 … HT02 (L1.ⓛW1) … (L2.ⓛW2)) [|*: /2 width=1 by fqup_fpbg, lpr_pair/ ] +#T #HT1 #HT2 -L0 -V0 -W0 -T0 +lapply (lsubr_cpms_trans … HT1 (L1.ⓓⓝW1.V1) ?) -HT1 /2 width=1 by lsubr_beta/ #HT1 +lapply (lsubr_cpms_trans … HT2 (L2.ⓓⓝW2.V2) ?) -HT2 /2 width=1 by lsubr_beta/ #HT2 +/4 width=5 by cpms_bind_dx, cpm_eps, ex2_intro/ +qed-. + +fact cnv_cpm_conf_lpr_theta_theta_aux (a) (h) (o) (p) (G) (L) (V) (W) (T): + (∀G0,L0,T0. ⦃G,L,ⓐV.ⓓ{p}W.T⦄ >[h,o] ⦃G0,L0,T0⦄ → IH_cnv_cpms_conf_lpr a h G0 L0 T0) → + ⦃G,L⦄ ⊢ ⓐV.ⓓ{p}W.T ![a,h] → + ∀V1. ⦃G,L⦄ ⊢ V ➡[h] V1 → ∀V2. ⦃G,L⦄ ⊢ V ➡[h] V2 → + ∀W1. ⦃G,L⦄ ⊢ W ➡[h] W1 → ∀W2. ⦃G,L⦄ ⊢ W ➡[h] W2 → + ∀n1,T1. ⦃G,L.ⓓW⦄ ⊢ T ➡[n1,h] T1 → ∀n2,T2. ⦃G,L.ⓓW⦄ ⊢ T ➡[n2,h] T2 → + ∀U1. ⬆*[1]V1 ≘ U1 → ∀U2. ⬆*[1]V2 ≘ U2 → + ∀L1. ⦃G,L⦄ ⊢ ➡[h] L1 → ∀L2. ⦃G,L⦄ ⊢ ➡[h] L2 → + ∃∃T. ⦃G,L1⦄ ⊢ ⓓ{p}W1.ⓐU1.T1 ➡*[n2-n1,h] T & ⦃G,L2⦄ ⊢ ⓓ{p}W2.ⓐU2.T2 ➡*[n1-n2,h] T. +#a #h #o #p #G0 #L0 #V0 #W0 #T0 #IH #H0 +#V1 #HV01 #V2 #HV02 #W1 #HW01 #W2 #HW02 #n1 #T1 #HT01 #n2 #T2 #HT02 #U1 #HVU1 #U2 #HVU2 +#L1 #HL01 #L2 #HL02 +elim (cnv_inv_appl … H0) -H0 #n0 #p0 #X01 #X02 #_ #HV0 #H0 #_ #_ -n0 -p0 -X01 -X02 +elim (cnv_inv_bind … H0) -H0 #HW0 #HT0 +elim (cpr_conf_lpr … HV01 … HV02 … HL01 … HL02) #V #HV1 #HV2 +elim (cpr_conf_lpr … HW01 … HW02 … HL01 … HL02) #W #HW1 #HW2 +elim (cnv_cpm_conf_lpr_far … IH … HT01 … HT02 (L1.ⓓW1) … (L2.ⓓW2)) [|*: /2 width=1 by fqup_fpbg, lpr_pair/ ] +#T #HT1 #HT2 -L0 -V0 -W0 -T0 +elim (cpm_lifts_sn … HV1 (Ⓣ) … (L1.ⓓW1) … HVU1) -V1 [| /3 width=1 by drops_refl, drops_drop/ ] #U #HVU #HU1 +lapply (cpm_lifts_bi … HV2 (Ⓣ) … (L2.ⓓW2) … HVU2 … HVU) -V2 -V [ /3 width=1 by drops_refl, drops_drop/ ] #HU2 +/4 width=7 by cpms_appl_dx, cpms_bind_dx, ex2_intro/ +qed-. + +fact cnv_cpm_conf_lpr_cast_cast_aux (a) (h) (o) (G) (L) (V) (T): + (∀G0,L0,T0. ⦃G,L,ⓝV.T⦄ >[h,o] ⦃G0,L0,T0⦄ → IH_cnv_cpms_conf_lpr a h G0 L0 T0) → + ⦃G,L⦄ ⊢ ⓝV.T ![a,h] → + ∀n1,V1. ⦃G,L⦄ ⊢ V ➡[n1,h] V1 → ∀n2,V2. ⦃G,L⦄ ⊢ V ➡[n2,h] V2 → + ∀T1. ⦃G,L⦄ ⊢ T ➡[n1,h] T1 → ∀T2. ⦃G,L⦄ ⊢ T ➡[n2,h] T2 → + ∀L1. ⦃G,L⦄ ⊢ ➡[h] L1 → ∀L2. ⦃G,L⦄ ⊢ ➡[h] L2 → + ∃∃T. ⦃G,L1⦄ ⊢ ⓝV1.T1 ➡*[n2-n1,h] T & ⦃G,L2⦄ ⊢ ⓝV2.T2 ➡*[n1-n2,h] T. +#a #h #o #G0 #L0 #V0 #T0 #IH #H0 +#n1 #V1 #HV01 #n2 #V2 #HV02 #T1 #HT01 #T2 #HT02 +#L1 #HL01 #L2 #HL02 +elim (cnv_inv_cast … H0) -H0 #X0 #HV0 #HT0 #_ #_ -X0 +elim (cnv_cpm_conf_lpr_far … IH … HV01 … HV02 … HL01 … HL02) [|*: /2 width=1 by fqup_fpbg/ ] +elim (cnv_cpm_conf_lpr_far … IH … HT01 … HT02 … HL01 … HL02) [|*: /2 width=1 by fqup_fpbg/ ] +#T #HT1 #HT2 #V #HV1 #HV2 -L0 -V0 -T0 +/3 width=5 by cpms_cast, ex2_intro/ +qed-. + +fact cnv_cpm_conf_lpr_cast_epsilon_aux (a) (h) (o) (G) (L) (V) (T): + (∀G0,L0,T0. ⦃G,L,ⓝV.T⦄ >[h,o] ⦃G0,L0,T0⦄ → IH_cnv_cpms_conf_lpr a h G0 L0 T0) → + ⦃G,L⦄ ⊢ ⓝV.T ![a,h] → + ∀n1,V1. ⦃G,L⦄ ⊢ V ➡[n1,h] V1 → + ∀T1. ⦃G,L⦄ ⊢ T ➡[n1,h] T1 → ∀n2,T2. ⦃G,L⦄ ⊢ T ➡[n2,h] T2 → + ∀L1. ⦃G,L⦄ ⊢ ➡[h] L1 → ∀L2. ⦃G,L⦄ ⊢ ➡[h] L2 → + ∃∃T. ⦃G,L1⦄ ⊢ ⓝV1.T1 ➡*[n2-n1,h] T & ⦃G,L2⦄ ⊢ T2 ➡*[n1-n2,h] T. +#a #h #o #G0 #L0 #V0 #T0 #IH #H0 +#n1 #V1 #HV01 #T1 #HT01 #n2 #T2 #HT02 +#L1 #HL01 #L2 #HL02 +elim (cnv_inv_cast … H0) -H0 #X0 #HV0 #HT0 #_ #_ -X0 +elim (cnv_cpm_conf_lpr_far … IH … HT01 … HT02 … HL01 … HL02) [|*: /2 width=1 by fqup_fpbg/ ] +#T #HT1 #HT2 -L0 -V0 -T0 +/3 width=3 by cpms_eps, ex2_intro/ +qed-. + +fact cnv_cpm_conf_lpr_cast_ee_aux (a) (h) (o) (G) (L) (V) (T): + (∀G0,L0,T0. ⦃G,L,ⓝV.T⦄ >[h,o] ⦃G0,L0,T0⦄ → IH_cnv_cpm_trans_lpr a h G0 L0 T0) → + (∀G0,L0,T0. ⦃G,L,ⓝV.T⦄ >[h,o] ⦃G0,L0,T0⦄ → IH_cnv_cpms_conf_lpr a h G0 L0 T0) → + ⦃G,L⦄ ⊢ ⓝV.T ![a,h] → + ∀n1,V1. ⦃G,L⦄ ⊢ V ➡[n1,h] V1 → ∀n2,V2. ⦃G,L⦄ ⊢ V ➡[n2,h] V2 → + ∀T1. ⦃G,L⦄ ⊢ T ➡[n1,h] T1 → + ∀L1. ⦃G,L⦄ ⊢ ➡[h] L1 → ∀L2. ⦃G,L⦄ ⊢ ➡[h] L2 → + ∃∃T. ⦃G,L1⦄ ⊢ ⓝV1.T1 ➡*[↑n2-n1,h] T & ⦃G,L2⦄ ⊢ V2 ➡*[n1-↑n2,h] T. +#a #h #o #G0 #L0 #V0 #T0 #IH2 #IH1 #H0 +#n1 #V1 #HV01 #n2 #V2 #HV02 #T1 #HT01 +#L1 #HL01 #L2 #HL02 -HV01 +elim (cnv_inv_cast … H0) -H0 #X0 #HV0 #HT0 #HVX0 #HTX0 +lapply (cnv_cpms_trans_lpr_far … IH2 … HVX0 … L0 ?) [4:|*: /2 width=1 by fqup_fpbg/ ] #HX0 +elim (cnv_cpms_strip_lpr_far … IH1 … HVX0 … HV02 … L0 … HL02) [|*: /2 width=1 by fqup_fpbg/ ] +elim (cnv_cpms_strip_lpr_far … IH1 … HTX0 … HT01 … L0 … HL01) [|*: /2 width=1 by fqup_fpbg/ ] +-HV02 -HTX0 -HT01 minus_plus #H2 +lapply (cpms_trans … HT1 … HTU) -T [h,o] ⦃G0,L0,T0⦄ → IH_cnv_cpms_conf_lpr a h G0 L0 T0) → + ⦃G,L⦄ ⊢ ⓝV.T ![a,h] → + ∀n1,T1. ⦃G,L⦄ ⊢ T ➡[n1,h] T1 → ∀n2,T2. ⦃G,L⦄ ⊢ T ➡[n2,h] T2 → + ∀L1. ⦃G,L⦄ ⊢ ➡[h] L1 → ∀L2. ⦃G,L⦄ ⊢ ➡[h] L2 → + ∃∃T. ⦃G,L1⦄ ⊢ T1 ➡*[n2-n1,h] T & ⦃G,L2⦄ ⊢ T2 ➡*[n1-n2,h] T. +#a #h #o #G0 #L0 #V0 #T0 #IH #H0 +#n1 #T1 #HT01 #n2 #T2 #HT02 +#L1 #HL01 #L2 #HL02 +elim (cnv_inv_cast … H0) -H0 #X0 #_ #HT0 #_ #_ -X0 +elim (cnv_cpm_conf_lpr_far … IH … HT01 … HT02 … HL01 … HL02) [|*: /2 width=1 by fqup_fpbg/ ] +#T #HT1 #HT2 -L0 -V0 -T0 +/2 width=3 by ex2_intro/ +qed-. + +fact cnv_cpm_conf_lpr_epsilon_ee_aux (a) (h) (o) (G) (L) (V) (T): + (∀G0,L0,T0. ⦃G,L,ⓝV.T⦄ >[h,o] ⦃G0,L0,T0⦄ → IH_cnv_cpm_trans_lpr a h G0 L0 T0) → + (∀G0,L0,T0. ⦃G,L,ⓝV.T⦄ >[h,o] ⦃G0,L0,T0⦄ → IH_cnv_cpms_conf_lpr a h G0 L0 T0) → + ⦃G,L⦄ ⊢ ⓝV.T ![a,h] → + ∀n1,T1. ⦃G,L⦄ ⊢ T ➡[n1,h] T1 → ∀n2,V2. ⦃G,L⦄ ⊢ V ➡[n2,h] V2 → + ∀L1. ⦃G,L⦄ ⊢ ➡[h] L1 → ∀L2. ⦃G,L⦄ ⊢ ➡[h] L2 → + ∃∃T. ⦃G,L1⦄ ⊢ T1 ➡*[↑n2-n1,h] T & ⦃G,L2⦄ ⊢ V2 ➡*[n1-↑n2,h] T. +#a #h #o #G0 #L0 #V0 #T0 #IH2 #IH1 #H0 +#n1 #T1 #HT01 #n2 #V2 #HV02 +#L1 #HL01 #L2 #HL02 +elim (cnv_inv_cast … H0) -H0 #X0 #HV0 #HT0 #HVX0 #HTX0 +lapply (cnv_cpms_trans_lpr_far … IH2 … HVX0 … L0 ?) [4:|*: /2 width=1 by fqup_fpbg/ ] #HX0 +elim (cnv_cpms_strip_lpr_far … IH1 … HVX0 … HV02 … L0 … HL02) [|*: /2 width=1 by fqup_fpbg/ ] +elim (cnv_cpms_strip_lpr_far … IH1 … HTX0 … HT01 … L0 … HL01) [|*: /2 width=1 by fqup_fpbg/ ] +-HV02 -HTX0 -HT01 minus_plus #H2 +lapply (cpms_trans … HT1 … HTU) -T [h,o] ⦃G0,L0,T0⦄ → IH_cnv_cpms_conf_lpr a h G0 L0 T0) → + ⦃G,L⦄ ⊢ ⓝV.T ![a,h] → + ∀n1,V1. ⦃G,L⦄ ⊢ V ➡[n1,h] V1 → ∀n2,V2. ⦃G,L⦄ ⊢ V ➡[n2,h] V2 → + ∀L1. ⦃G,L⦄ ⊢ ➡[h] L1 → ∀L2. ⦃G,L⦄ ⊢ ➡[h] L2 → + ∃∃T. ⦃G,L1⦄ ⊢ V1 ➡*[n2-n1,h] T & ⦃G,L2⦄ ⊢ V2 ➡*[n1-n2,h] T. +#a #h #o #G0 #L0 #V0 #T0 #IH #H0 +#n1 #V1 #HV01 #n2 #V2 #HV02 +#L1 #HL01 #L2 #HL02 +elim (cnv_inv_cast … H0) -H0 #X0 #HV0 #_ #_ #_ -X0 +elim (cnv_cpm_conf_lpr_far … IH … HV01 … HV02 … HL01 … HL02) [|*: /2 width=1 by fqup_fpbg/ ] +#V #HV1 #HV2 -L0 -V0 -T0 +/2 width=3 by ex2_intro/ +qed-. + +fact cnv_cpm_conf_lpr_aux (a) (h) (o): + ∀G0,L0,T0. + (∀G1,L1,T1. ⦃G0, L0, T0⦄ >[h, o] ⦃G1, L1, T1⦄ → IH_cnv_cpm_trans_lpr a h G1 L1 T1) → + (∀G1,L1,T1. ⦃G0, L0, T0⦄ >[h, o] ⦃G1, L1, T1⦄ → IH_cnv_cpms_conf_lpr a h G1 L1 T1) → + ∀G1,L1,T1. G0 = G1 → L0 = L1 → T0 = T1 → IH_cnv_cpm_conf_lpr a h G1 L1 T1. +#a #h #o #G0 #L0 #T0 #IH2 #IH1 #G #L * [| * [| * ]] +[ #I #HG0 #HL0 #HT0 #HT #n1 #X1 #HX1 #n2 #X2 #HX2 #L1 #HL1 #L2 #HL2 destruct + elim (cpm_inv_atom1_drops … HX1) -HX1 * + elim (cpm_inv_atom1_drops … HX2) -HX2 * + [ #H21 #H22 #H11 #H12 destruct -L -a -o + minus_S_S >minus_S_S + @(cnv_cpm_conf_lpr_delta_delta_aux … IH1) -IH1 /1 width=13 by/ + ] +| #p #I #V #T #HG0 #HL0 #HT0 #HT #n1 #X1 #HX1 #n2 #X2 #HX2 #L1 #HL1 #L2 #HL2 destruct + elim (cpm_inv_bind1 … HX1) -HX1 * + elim (cpm_inv_bind1 … HX2) -HX2 * + [ #V2 #T2 #HV2 #HT2 #H21 #V1 #T1 #HV1 #HT1 #H11 destruct -IH2 + @(cnv_cpm_conf_lpr_bind_bind_aux … IH1) -IH1 /1 width=1 by/ + | #T2 #HT2 #HXT2 #H21 #H22 #V1 #T1 #HV1 #HT1 #H11 destruct -IH2 + @(cnv_cpm_conf_lpr_bind_zeta_aux … IH1) -IH1 /1 width=3 by/ + | #V2 #T2 #HV2 #HT2 #H21 #T1 #HT1 #HXT1 #H11 #H12 destruct -IH2 + @ex2_commute @(cnv_cpm_conf_lpr_bind_zeta_aux … IH1) -IH1 /1 width=3 by/ + | #T2 #HT2 #HXT2 #H21 #H22 #T1 #HT1 #HXT1 #H11 #H12 destruct -IH2 + @(cnv_cpm_conf_lpr_zeta_zeta_aux … IH1) -IH1 /1 width=3 by/ + ] +| #V #T #HG0 #HL0 #HT0 #HT #n1 #X1 #HX1 #n2 #X2 #HX2 #L1 #HL1 #L2 #HL2 destruct + elim (cpm_inv_appl1 … HX1) -HX1 * + elim (cpm_inv_appl1 … HX2) -HX2 * + [ #V2 #T2 #HV2 #HT2 #H21 #V1 #T1 #HV1 #HT1 #H11 destruct -IH2 + @(cnv_cpm_conf_lpr_appl_appl_aux … IH1) -IH1 /1 width=1 by/ + | #p2 #V2 #XW2 #W2 #XT2 #T2 #HV2 #HW2 #HT2 #H21 #H22 #V1 #T1 #HV1 #HT1 #H11 destruct -IH2 + @(cnv_cpm_conf_lpr_appl_beta_aux … IH1) -IH1 /1 width=1 by/ + | #p2 #V2 #XV2 #XW2 #W2 #XT2 #T2 #HV2 #HXV2 #HW2 #HT2 #H21 #H22 #V1 #T1 #HV1 #HT1 #H11 destruct -IH2 + @(cnv_cpm_conf_lpr_appl_theta_aux … IH1) -IH1 /1 width=3 by/ + | #V2 #T2 #HV2 #HT2 #H21 #p1 #V1 #XW1 #W1 #XT1 #T1 #HV1 #HW1 #HT1 #H11 #H12 destruct -IH2 + @ex2_commute @(cnv_cpm_conf_lpr_appl_beta_aux … IH1) -IH1 /1 width=1 by/ + | #p2 #V2 #XW2 #W2 #XT2 #T2 #HV2 #HW2 #HT2 #H21 #H22 #p1 #V1 #XW1 #W1 #XT1 #T1 #HV1 #HW1 #HT1 #H11 #H12 destruct -IH2 + @(cnv_cpm_conf_lpr_beta_beta_aux … IH1) -IH1 /1 width=1 by/ + | #p2 #V2 #XV2 #XW2 #W2 #XT2 #T2 #HV2 #HXV2 #HW2 #HT2 #H21 #H22 #p1 #V1 #XW1 #W1 #XT1 #T1 #HV1 #HW1 #HT1 #H11 #H12 destruct + | #V2 #T2 #HV2 #HT2 #H21 #p1 #V1 #XV1 #XW1 #W1 #XT1 #T1 #HV1 #HXV1 #HW1 #HT1 #H11 #H12 destruct -IH2 + @ex2_commute @(cnv_cpm_conf_lpr_appl_theta_aux … IH1) -IH1 /1 width=3 by/ + | #p2 #V2 #XW2 #W2 #XT2 #T2 #HV2 #HW2 #HT2 #H21 #H22 #p1 #V1 #XV1 #XW1 #W1 #XT1 #T1 #HV1 #HXV1 #HW1 #HT1 #H11 #H12 destruct + | #p2 #V2 #XV2 #XW2 #W2 #XT2 #T2 #HV2 #HXV2 #HW2 #HT2 #H21 #H22 #p1 #V1 #XV1 #XW1 #W1 #XT1 #T1 #HV1 #HXV1 #HW1 #HT1 #H11 #H12 destruct -IH2 + @(cnv_cpm_conf_lpr_theta_theta_aux … IH1) -IH1 /1 width=3 by/ + ] +| #V #T #HG0 #HL0 #HT0 #HT #n1 #X1 #HX1 #n2 #X2 #HX2 #L1 #HL1 #L2 #HL2 destruct + elim (cpm_inv_cast1 … HX1) -HX1 [ * || * ] + elim (cpm_inv_cast1 … HX2) -HX2 [ * || * | * || * | * || * ] + [ #V2 #T2 #HV2 #HT2 #H21 #V1 #T1 #HV1 #HT1 #H11 destruct -IH2 + @(cnv_cpm_conf_lpr_cast_cast_aux … IH1) -IH1 /1 width=1 by/ + | #HT2 #V1 #T1 #HV1 #HT1 #H11 destruct -IH2 + @(cnv_cpm_conf_lpr_cast_epsilon_aux … IH1) -IH1 /1 width=1 by/ + | #m2 #HV2 #H21 #V1 #T1 #HV1 #HT1 #H11 destruct + @(cnv_cpm_conf_lpr_cast_ee_aux … IH2 IH1) -IH2 -IH1 /1 width=1 by/ + | #V2 #T2 #HV2 #HT2 #H21 #HT1 destruct -IH2 + @ex2_commute @(cnv_cpm_conf_lpr_cast_epsilon_aux … IH1) -IH1 /1 width=1 by/ + | #HT2 #HT1 -IH2 + @(cnv_cpm_conf_lpr_epsilon_epsilon_aux … IH1) -IH1 /1 width=1 by/ + | #m2 #HV2 #H21 #HT1 destruct + @(cnv_cpm_conf_lpr_epsilon_ee_aux … IH2 IH1) -IH2 -IH1 /1 width=1 by/ + | #V2 #T2 #HV2 #HT2 #H21 #m1 #HV1 #H11 destruct + @ex2_commute @(cnv_cpm_conf_lpr_cast_ee_aux … IH2 IH1) -IH2 -IH1 /1 width=1 by/ + | #HT2 #m1 #HV1 #H11 destruct + @ex2_commute @(cnv_cpm_conf_lpr_epsilon_ee_aux … IH2 IH1) -IH2 -IH1 /1 width=1 by/ + | #m2 #HV2 #H21 #m1 #HV1 #H11 destruct -IH2 + >minus_S_S >minus_S_S + @(cnv_cpm_conf_lpr_ee_ee_aux … IH1) -IH1 /1 width=1 by/ + ] +] +qed-. diff --git a/matita/matita/contribs/lambdadelta/basic_2/dynamic/cnv_cpm_trans.ma b/matita/matita/contribs/lambdadelta/basic_2/dynamic/cnv_cpm_trans.ma index 29d40c3ef..a40f4fa60 100644 --- a/matita/matita/contribs/lambdadelta/basic_2/dynamic/cnv_cpm_trans.ma +++ b/matita/matita/contribs/lambdadelta/basic_2/dynamic/cnv_cpm_trans.ma @@ -16,12 +16,12 @@ include "basic_2/rt_computation/cpms_fpbg.ma". include "basic_2/rt_computation/cprs_cprs.ma". include "basic_2/rt_computation/lprs_cpms.ma". include "basic_2/dynamic/cnv_drops.ma". -include "basic_2/dynamic/cnv_etc.ma". +include "basic_2/dynamic/cnv_preserve_far.ma". include "basic_2/dynamic/lsubv_cnv.ma". (* CONTEXT-SENSITIVE NATIVE VALIDITY FOR TERMS ******************************) -(* Properties with context-free parallel reduction for local environments *****) +(* Far preservation propery with t-bound rt-transition for terms ************) fact cnv_cpm_trans_lpr_aux (a) (h) (o): ∀G0,L0,T0. @@ -118,7 +118,7 @@ fact cnv_cpm_trans_lpr_aux (a) (h) (o): elim (IH2 … HXUW1 … HXUT1 … HL12 … HL12) [|*: /2 width=4 by fqup_cpms_fwd_fpbg/ ] -HXUW1 -HXUT1 -HWU1 >eq_minus_O // #W0 #H1 #H2 -IH2 -IH1 -L1 -W1 -T1 -U1 lapply (cprs_trans … HXW21 … H1) -XW1 #H1 - lapply (cpms_trans … HXT21 … H2) -XT1 [h, o] ⦃G1, L1, T1⦄ → IH_cnv_cpm_trans_lpr a h G1 L1 T1) → - ∀G1,L1,T1. ⦃G0, L0, T0⦄ >[h, o] ⦃G1, L1, T1⦄ → IH_cnv_cpms_trans_lpr a h G1 L1 T1. -#a #h #o #G0 #L0 #T0 #IH #G1 #L1 #T1 #H01 #HT1 #n #T2 #H -@(cpms_ind_dx … H) -n -T2 -/4 width=7 by cpms_fwd_fpbs, fpbg_fpbs_trans/ -qed-. - -lemma cnv_cpms_strip_lpr_far (a) (h) (o): - ∀G0,L0,T0. - (∀G1,L1,T1. ⦃G0, L0, T0⦄ >[h, o] ⦃G1, L1, T1⦄ → IH_cnv_cpms_conf_lpr a h G1 L1 T1) → - ∀G1,L1,T1. ⦃G0, L0, T0⦄ >[h, o] ⦃G1, L1, T1⦄ → IH_cnv_cpms_strip_lpr a h G1 L1 T1. -/3 width=8 by cpm_cpms/ qed-. - -(* -fact cnv_cpms_strip_lpr_aux (a) (h) (o): - ∀G0,L0,T0. - (∀G1,L1,T1. ⦃G0, L0, T0⦄ >[h, o] ⦃G1, L1, T1⦄ → IH_cnv_cpm_conf_lpr a h G1 L1 T1) → - ∀G1,L1,T1. ⦃G0, L0, T0⦄ >[h, o] ⦃G1, L1, T1⦄ → IH_cnv_cpms_strip_lpr a h G1 L1 T1. -#a #h #o #G0 #L0 #T0 #IH0 #G #L #T #H0 #HT #n1 #T1 #H -generalize in match HT; generalize in match H0; -H0 -HT -@(cpms_ind_sn … H) -n1 -T [ /2 width=8 by/ ] -#n1 #n2 #T #X #HTX #HXT1 #IH #H0 #HT #n2 #T2 #HT2 #L1 #HL1 #L2 #HL2 -elim (IH0 … HTX … HT2 … HL1 … HL2) // -L -T #T0 #HXT0 #HT20 - - @(IH … 0 T … HT2 … HL1 … HL2) // -L -IH - #T0 #HT20 #HT0 -*) diff --git a/matita/matita/contribs/lambdadelta/basic_2/dynamic/cnv_preserve_far.ma b/matita/matita/contribs/lambdadelta/basic_2/dynamic/cnv_preserve_far.ma new file mode 100644 index 000000000..e8f2c8e2f --- /dev/null +++ b/matita/matita/contribs/lambdadelta/basic_2/dynamic/cnv_preserve_far.ma @@ -0,0 +1,72 @@ +(**************************************************************************) +(* ___ *) +(* ||M|| *) +(* ||A|| A project by Andrea Asperti *) +(* ||T|| *) +(* ||I|| Developers: *) +(* ||T|| The HELM team. *) +(* ||A|| http://helm.cs.unibo.it *) +(* \ / *) +(* \ / This file is distributed under the terms of the *) +(* v GNU General Public License Version 2 *) +(* *) +(**************************************************************************) + +include "basic_2/rt_computation/fpbg.ma". +include "basic_2/rt_computation/cpms_fpbs.ma". +include "basic_2/dynamic/cnv.ma". + +(* CONTEXT-SENSITIVE NATIVE VALIDITY FOR TERMS ******************************) + +(* Inductive premises for the preservation results **************************) + +definition IH_cnv_cpm_trans_lpr (a) (h): relation3 genv lenv term ≝ + λG,L1,T1. ⦃G, L1⦄ ⊢ T1 ![a,h] → + ∀n,T2. ⦃G, L1⦄ ⊢ T1 ➡[n,h] T2 → + ∀L2. ⦃G, L1⦄ ⊢ ➡[h] L2 → ⦃G, L2⦄ ⊢ T2 ![a,h]. + +definition IH_cnv_cpms_trans_lpr (a) (h): relation3 genv lenv term ≝ + λG,L1,T1. ⦃G, L1⦄ ⊢ T1 ![a,h] → + ∀n,T2. ⦃G, L1⦄ ⊢ T1 ➡*[n,h] T2 → + ∀L2. ⦃G, L1⦄ ⊢ ➡[h] L2 → ⦃G, L2⦄ ⊢ T2 ![a,h]. + +definition IH_cnv_cpm_conf_lpr (a) (h): relation3 genv lenv term ≝ + λG,L0,T0. ⦃G, L0⦄ ⊢ T0 ![a,h] → + ∀n1,T1. ⦃G, L0⦄ ⊢ T0 ➡[n1,h] T1 → ∀n2,T2. ⦃G, L0⦄ ⊢ T0 ➡[n2,h] T2 → + ∀L1. ⦃G, L0⦄ ⊢ ➡[h] L1 → ∀L2. ⦃G, L0⦄ ⊢ ➡[h] L2 → + ∃∃T. ⦃G, L1⦄ ⊢ T1 ➡*[n2-n1,h] T & ⦃G, L2⦄ ⊢ T2 ➡*[n1-n2,h] T. + +definition IH_cnv_cpms_strip_lpr (a) (h): relation3 genv lenv term ≝ + λG,L0,T0. ⦃G, L0⦄ ⊢ T0 ![a,h] → + ∀n1,T1. ⦃G, L0⦄ ⊢ T0 ➡*[n1,h] T1 → ∀n2,T2. ⦃G, L0⦄ ⊢ T0 ➡[n2,h] T2 → + ∀L1. ⦃G, L0⦄ ⊢ ➡[h] L1 → ∀L2. ⦃G, L0⦄ ⊢ ➡[h] L2 → + ∃∃T. ⦃G, L1⦄ ⊢ T1 ➡*[n2-n1,h] T & ⦃G, L2⦄ ⊢ T2 ➡*[n1-n2,h] T. + +definition IH_cnv_cpms_conf_lpr (a) (h): relation3 genv lenv term ≝ + λG,L0,T0. ⦃G, L0⦄ ⊢ T0 ![a,h] → + ∀n1,T1. ⦃G, L0⦄ ⊢ T0 ➡*[n1,h] T1 → ∀n2,T2. ⦃G, L0⦄ ⊢ T0 ➡*[n2,h] T2 → + ∀L1. ⦃G, L0⦄ ⊢ ➡[h] L1 → ∀L2. ⦃G, L0⦄ ⊢ ➡[h] L2 → + ∃∃T. ⦃G, L1⦄ ⊢ T1 ➡*[n2-n1,h] T & ⦃G, L2⦄ ⊢ T2 ➡*[n1-n2,h] T. + +(* Properties for preservation **********************************************) + +lemma cnv_cpms_trans_lpr_far (a) (h) (o): + ∀G0,L0,T0. + (∀G1,L1,T1. ⦃G0, L0, T0⦄ >[h, o] ⦃G1, L1, T1⦄ → IH_cnv_cpm_trans_lpr a h G1 L1 T1) → + ∀G1,L1,T1. ⦃G0, L0, T0⦄ >[h, o] ⦃G1, L1, T1⦄ → IH_cnv_cpms_trans_lpr a h G1 L1 T1. +#a #h #o #G0 #L0 #T0 #IH #G1 #L1 #T1 #H01 #HT1 #n #T2 #H +@(cpms_ind_dx … H) -n -T2 +/4 width=7 by cpms_fwd_fpbs, fpbg_fpbs_trans/ +qed-. + +lemma cnv_cpm_conf_lpr_far (a) (h) (o): + ∀G0,L0,T0. + (∀G1,L1,T1. ⦃G0, L0, T0⦄ >[h, o] ⦃G1, L1, T1⦄ → IH_cnv_cpms_conf_lpr a h G1 L1 T1) → + ∀G1,L1,T1. ⦃G0, L0, T0⦄ >[h, o] ⦃G1, L1, T1⦄ → IH_cnv_cpm_conf_lpr a h G1 L1 T1. +/3 width=8 by cpm_cpms/ qed-. + +lemma cnv_cpms_strip_lpr_far (a) (h) (o): + ∀G0,L0,T0. + (∀G1,L1,T1. ⦃G0, L0, T0⦄ >[h, o] ⦃G1, L1, T1⦄ → IH_cnv_cpms_conf_lpr a h G1 L1 T1) → + ∀G1,L1,T1. ⦃G0, L0, T0⦄ >[h, o] ⦃G1, L1, T1⦄ → IH_cnv_cpms_strip_lpr a h G1 L1 T1. +/3 width=8 by cpm_cpms/ qed-. diff --git a/matita/matita/contribs/lambdadelta/basic_2/dynamic/lsubv.ma b/matita/matita/contribs/lambdadelta/basic_2/dynamic/lsubv.ma index 6549c361e..20b5259d0 100644 --- a/matita/matita/contribs/lambdadelta/basic_2/dynamic/lsubv.ma +++ b/matita/matita/contribs/lambdadelta/basic_2/dynamic/lsubv.ma @@ -109,3 +109,8 @@ qed-. lemma lsubv_refl (a) (h) (G): reflexive … (lsubv a h G). #a #h #G #L elim L -L /2 width=1 by lsubv_atom, lsubv_bind/ qed. + +(* Basic_2A1: removed theorems 3: + lsubsv_lstas_trans lsubsv_sta_trans + lsubsv_fwd_lsubd +*) diff --git a/matita/matita/contribs/lambdadelta/basic_2/dynamic/partial.txt b/matita/matita/contribs/lambdadelta/basic_2/dynamic/partial.txt index 361be816f..f4923619f 100644 --- a/matita/matita/contribs/lambdadelta/basic_2/dynamic/partial.txt +++ b/matita/matita/contribs/lambdadelta/basic_2/dynamic/partial.txt @@ -1,3 +1,3 @@ cnv.ma cnv_drops.ma cnv_fqus.ma cnv_aaa.ma cnv_fsb.ma -cnv_etc.ma cnv_cpm_trans.ma +cnv_preserve_far.ma cnv_cpm_trans.ma cnv_cpm_conf.ma lsubv.ma lsubv_drops.ma lsubv_lsubr.ma lsubv_lsuba.ma lsubv_cpms.ma lsubv_cpcs.ma lsubv_cnv.ma lsubv_lsubv.ma diff --git a/matita/matita/contribs/lambdadelta/basic_2/dynamic/snv_da_lpr.ma b/matita/matita/contribs/lambdadelta/basic_2/dynamic/snv_da_lpr.ma deleted file mode 100644 index e4f1699fd..000000000 --- a/matita/matita/contribs/lambdadelta/basic_2/dynamic/snv_da_lpr.ma +++ /dev/null @@ -1,92 +0,0 @@ -(**************************************************************************) -(* ___ *) -(* ||M|| *) -(* ||A|| A project by Andrea Asperti *) -(* ||T|| *) -(* ||I|| Developers: *) -(* ||T|| The HELM team. *) -(* ||A|| http://helm.cs.unibo.it *) -(* \ / *) -(* \ / This file is distributed under the terms of the *) -(* v GNU General Public License Version 2 *) -(* *) -(**************************************************************************) - -include "static_2/static/lsubd_da.ma". -include "basic_2/dynamic/snv_aaa.ma". -include "basic_2/dynamic/snv_scpes.ma". - -(* STRATIFIED NATIVE VALIDITY FOR TERMS *************************************) - -(* Properties on degree assignment for terms ********************************) - -fact da_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 = G1 → L0 = L1 → T0 = T1 → IH_da_cpr_lpr h o G1 L1 T1. -#h #o #G0 #L0 #T0 #IH3 #IH2 #IH1 #G1 #L1 * * [|||| * ] -[ #s #_ #_ #_ #_ #d #H2 #X3 #H3 #L2 #_ -IH3 -IH2 -IH1 - lapply (da_inv_sort … H2) -H2 - lapply (cpr_inv_sort1 … H3) -H3 #H destruct /2 width=1 by da_sort/ -| #i #HG0 #HL0 #HT0 #H1 #d #H2 #X3 #H3 #L2 #HL12 destruct -IH3 -IH2 - elim (snv_inv_lref … H1) -H1 #I0 #K0 #X0 #H #HX0 - elim (da_inv_lref … H2) -H2 * #K1 [ #V1 | #W1 #d1 ] #HLK1 [ #HV1 | #HW1 #H ] destruct - lapply (drop_mono … H … HLK1) -H #H destruct - elim (cpr_inv_lref1 … H3) -H3 - [1,3: #H destruct - lapply (fqup_lref … G1 … HLK1) - elim (lpr_drop_conf … HLK1 … HL12) -HLK1 -HL12 #X #H #HLK2 - elim (lpr_inv_pair1 … H) -H #K2 #V2 #HK12 #HV12 #H destruct - /4 width=10 by da_ldef, da_ldec, fqup_fpbg/ - |2,4: * #K0 #V0 #W0 #H #HVW0 #HW0 - lapply (drop_mono … H … HLK1) -H #H destruct - lapply (fqup_lref … G1 … HLK1) - elim (lpr_drop_conf … HLK1 … HL12) -HLK1 -HL12 #X #H #HLK2 - elim (lpr_inv_pair1 … H) -H #K2 #V2 #HK12 #_ #H destruct - lapply (drop_fwd_drop2 … HLK2) -V2 - /4 width=8 by da_lift, fqup_fpbg/ - ] -| #p #_ #_ #HT0 #H1 destruct -IH3 -IH2 -IH1 - elim (snv_inv_gref … H1) -| #a #I #V1 #T1 #HG0 #HL0 #HT0 #H1 #d #H2 #X3 #H3 #L2 #HL12 destruct -IH2 - elim (snv_inv_bind … H1) -H1 #_ #HT1 - lapply (da_inv_bind … H2) -H2 - elim (cpr_inv_bind1 … H3) -H3 * - [ #V2 #T2 #HV12 #HT12 #H destruct - /4 width=9 by da_bind, fqup_fpbg, lpr_pair/ - | #T2 #HT12 #HT2 #H1 #H2 destruct - /4 width=11 by da_inv_lift, fqup_fpbg, lpr_pair, drop_drop/ - ] -| #V1 #T1 #HG0 #HL0 #HT0 #H1 #d #H2 #X3 #H3 #L2 #HL12 destruct - elim (snv_inv_appl … H1) -H1 #b1 #W1 #U1 #d1 #HV1 #HT1 #HVW1 #HTU1 - lapply (da_inv_flat … H2) -H2 #Hd - elim (cpr_inv_appl1 … H3) -H3 * - [ #V2 #T2 #HV12 #HT12 #H destruct -IH3 -IH2 /4 width=7 by da_flat, fqup_fpbg/ - | #b #V2 #W #W2 #U #U2 #HV12 #HW2 #HU2 #H1 #H2 destruct - elim (snv_inv_bind … HT1) -HT1 #HW #HU - lapply (da_inv_bind … Hd) -Hd #Hd - elim (scpds_inv_abst1 … HTU1) -HTU1 #W3 #U3 #HW3 #_ #H destruct -U3 -d1 - elim (snv_fwd_da … HV1) #d1 #Hd1 - elim (snv_fwd_da … HW) #d0 #Hd0 - lapply (cprs_scpds_div … HW3 … Hd0 … 1 HVW1) -W3 #H - elim (da_scpes_aux … IH3 IH2 IH1 … Hd0 … Hd1 … H) -IH3 -IH2 -H /2 width=1 by fqup_fpbg/ #_ #H1 - (plus_minus_k_k d1 1) in Hd1; // -H1 #Hd1 - lapply (IH1 … HV1 … Hd1 … HV12 … HL12) -HV1 -Hd1 -HV12 [ /2 by fqup_fpbg/ ] - lapply (IH1 … Hd0 … HW2 … HL12) -Hd0 /2 width=1 by fqup_fpbg/ -HW - lapply (IH1 … HU … Hd … HU2 (L2.ⓛW2) ?) -IH1 -HU -Hd -HU2 [1,2: /2 by fqup_fpbg, lpr_pair/ ] -HL12 -HW2 - /4 width=6 by da_bind, lsubd_da_trans, lsubd_beta/ - | #b #V0 #V2 #W #W2 #U #U2 #HV10 #HV02 #HW2 #HU2 #H1 #H2 destruct -IH3 -IH2 -b1 -V0 -W1 -U1 -d1 -HV1 - elim (snv_inv_bind … HT1) -HT1 #_ - lapply (da_inv_bind … Hd) -Hd - /5 width=9 by da_bind, da_flat, fqup_fpbg, lpr_pair/ - ] -| #W1 #T1 #HG0 #HL0 #HT0 #H1 #d #H2 #X3 #H3 #L2 #HL12 destruct -IH3 -IH2 - elim (snv_inv_cast … H1) -H1 #U1 #HW1 #HT1 #HWU1 #HTU1 - lapply (da_inv_flat … H2) -H2 #Hd - elim (cpr_inv_cast1 … H3) -H3 - [ * #W2 #T2 #HW12 #HT12 #H destruct /4 width=7 by da_flat, fqup_fpbg/ - | /3 width=7 by fqup_fpbg/ - ] -] -qed-. diff --git a/matita/matita/contribs/lambdadelta/basic_2/dynamic/snv_lstas.ma b/matita/matita/contribs/lambdadelta/basic_2/dynamic/snv_lstas.ma deleted file mode 100644 index 47c9cae13..000000000 --- a/matita/matita/contribs/lambdadelta/basic_2/dynamic/snv_lstas.ma +++ /dev/null @@ -1,58 +0,0 @@ -(**************************************************************************) -(* ___ *) -(* ||M|| *) -(* ||A|| A project by Andrea Asperti *) -(* ||T|| *) -(* ||I|| Developers: *) -(* ||T|| The HELM team. *) -(* ||A|| http://helm.cs.unibo.it *) -(* \ / *) -(* \ / This file is distributed under the terms of the *) -(* v GNU General Public License Version 2 *) -(* *) -(**************************************************************************) - -include "basic_2/dynamic/snv_lift.ma". -include "basic_2/dynamic/snv_scpes.ma". - -(* STRATIFIED NATIVE VALIDITY FOR TERMS *************************************) - -(* Properties on nat-iterated stratified static type assignment for terms ***) - -fact snv_lstas_aux: ∀h,o,G0,L0,T0. - (∀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, L0, T0⦄ >≛[h, o] ⦃G1, L1, T1⦄ → IH_snv_lstas h o G1 L1 T1) → - ∀G1,L1,T1. G0 = G1 → L0 = L1 → T0 = T1 → IH_snv_lstas h o G1 L1 T1. -#h #o #G0 #L0 #T0 #IH4 #IH3 #IH2 #IH1 #G1 #L1 * * [|||| * ] -[ #s #HG0 #HL0 #HT0 #_ #d1 #d2 #Hd21 #Hd1 #X #H2 destruct -IH4 -IH3 -IH2 -IH1 - >(lstas_inv_sort1 … H2) -X // -| #i #HG0 #HL0 #HT0 #H1 #d1 #d2 #Hd21 #Hd1 #T #H2 destruct -IH4 -IH3 -IH2 - elim (snv_inv_lref … H1) -H1 #I0 #K0 #X0 #HLK0 #HX0 - elim (da_inv_lref … Hd1) -Hd1 * #K1 [ #V1 | #W1 #d0 ] #HLK1 [ #Hd1 | #Hd0 #H ] - lapply (drop_mono … HLK0 … HLK1) -HLK0 #H0 destruct - elim (lstas_inv_lref1 … H2) -H2 * #K #Y #X [3,6: #d ] #HLK #HYX [1,2: #HXT #H0 |3,5: #HXT |4,6: #H1 #H2 ] - lapply (drop_mono … HLK … HLK1) -HLK #H destruct - [ lapply (le_plus_to_le_c … Hd21) -Hd21 #Hd21 |3: -Hd21 ] - lapply (fqup_lref … G1 … HLK1) #H - lapply (drop_fwd_drop2 … HLK1) /4 width=8 by snv_lift, snv_lref, fqup_fpbg/ -| #p #HG0 #HL0 #HT0 #H1 #d1 #d2 #Hd21 #Hd1 #X #H2 destruct -IH4 -IH3 -IH2 -IH1 - elim (snv_inv_gref … H1) -| #a #I #V1 #T1 #HG0 #HL0 #HT0 #H1 #d1 #d2 #Hd21 #Hd1 #X #H2 destruct -IH4 -IH3 -IH2 - elim (snv_inv_bind … H1) -H1 #HV1 #HT1 - lapply (da_inv_bind … Hd1) -Hd1 #Hd1 - elim (lstas_inv_bind1 … H2) -H2 #U1 #HTU1 #H destruct /4 width=8 by fqup_fpbg, snv_bind/ -| #V1 #T1 #HG0 #HL0 #HT0 #H1 #d1 #d2 #Hd21 #Hd1 #X #H2 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 #T0 #HT10 #H destruct - lapply (IH1 … HT1 … Hd1 … HT10) /2 width=1 by fqup_fpbg/ #HT0 - lapply (lstas_scpds_aux … IH1 IH4 IH3 IH2 … Hd1 … HT10 … HTU1) -IH4 -IH3 -IH2 -IH1 /2 width=1 by fqup_fpbg/ -T1 -d1 #H - elim (scpes_inv_abst2 … H) -H /3 width=6 by snv_appl, scpds_cprs_trans/ -| #U1 #T1 #HG0 #HL0 #HT0 #H1 #d1 #d2 #Hd21 #Hd1 #X #H2 destruct -IH4 -IH3 -IH2 - elim (snv_inv_cast … H1) -H1 - lapply (da_inv_flat … Hd1) -Hd1 - lapply (lstas_inv_cast1 … H2) -H2 /3 width=8 by fqup_fpbg/ -] -qed-. 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 deleted file mode 100644 index ed9b4e2fa..000000000 --- a/matita/matita/contribs/lambdadelta/basic_2/dynamic/snv_lstas_lpr.ma +++ /dev/null @@ -1,139 +0,0 @@ -(**************************************************************************) -(* ___ *) -(* ||M|| *) -(* ||A|| A project by Andrea Asperti *) -(* ||T|| *) -(* ||I|| Developers: *) -(* ||T|| The HELM team. *) -(* ||A|| http://helm.cs.unibo.it *) -(* \ / *) -(* \ / This file is distributed under the terms of the *) -(* v GNU General Public License Version 2 *) -(* *) -(**************************************************************************) - -include "basic_2/dynamic/snv_aaa.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,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 #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 … 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 #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_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 | #W2 | #V2 ] #HK12 [ #HW12 | #HW12 | #HV12 ] #H destruct - lapply (drop_fwd_drop2 … HLK2) #H2 - elim (cpr_inv_lref1 … H3) -H3 - [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 … 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_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 … 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 #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 … 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 … 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 … 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 #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 -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 … Hd1) -Hd1 #Hd1 - elim (lstas_inv_bind1 … HT1U) -HT1U #U #HT2U #H destruct - elim (scpds_inv_abst1 … HTU1) -HTU1 #W0 #U0 #HW20 #_ #H destruct -U0 -d0 - elim (snv_fwd_da … HW2) #d0 #HW2d - lapply (cprs_scpds_div … HW20 … HW2d … HVW1) -W0 #H21 - elim (snv_fwd_da … HV1) #d #HV1d - elim (da_scpes_aux … IH4 IH3 IH2 … HW2d … HV1d … H21) /2 width=1 by fqup_fpbg/ #_ #H - (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 (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_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 -d0 -W1 -HV1 -IH4 -IH3 -IH2 - elim (snv_inv_bind … HT1) -HT1 #_ #HT0 - 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 - lapply (cpcs_flat … HV10 … HU02 Appl) -HV10 -HU02 #HU02 - 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 #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 … Hd1 … HTU1 … HT12 … HL12) -IH1 -Hd1 -HTU1 -HL12 - /3 width=3 by fqup_fpbg, lstas_cast, ex2_intro/ - | #HT1X3 elim (IH1 … Hd1 … HTU1 … HT1X3 … HL12) -IH1 -Hd1 -HTU1 -HL12 - /2 width=3 by fqup_fpbg, ex2_intro/ - ] -] -qed-. diff --git a/matita/matita/contribs/lambdadelta/basic_2/dynamic/snv_preserve.etc b/matita/matita/contribs/lambdadelta/basic_2/dynamic/snv_preserve.etc new file mode 100644 index 000000000..482b94451 --- /dev/null +++ b/matita/matita/contribs/lambdadelta/basic_2/dynamic/snv_preserve.etc @@ -0,0 +1,94 @@ +(**************************************************************************) +(* ___ *) +(* ||M|| *) +(* ||A|| A project by Andrea Asperti *) +(* ||T|| *) +(* ||I|| Developers: *) +(* ||T|| The HELM team. *) +(* ||A|| http://helm.cs.unibo.it *) +(* \ / *) +(* \ / This file is distributed under the terms of the *) +(* v GNU General Public License Version 2 *) +(* *) +(**************************************************************************) + +include "basic_2/computation/fsb_aaa.ma". +include "basic_2/dynamic/snv_da_lpr.ma". +include "basic_2/dynamic/snv_lstas.ma". +include "basic_2/dynamic/snv_lstas_lpr.ma". +include "basic_2/dynamic/snv_lpr.ma". + +(* STRATIFIED NATIVE VALIDITY FOR TERMS *************************************) + +(* Main preservation properties *********************************************) + +lemma snv_preserve: ∀h,o,G,L,T. ⦃G, L⦄ ⊢ T ¡[h, o] → + ∧∧ IH_da_cpr_lpr h o G L T + & IH_snv_cpr_lpr h o G L T + & IH_snv_lstas h o G L T + & IH_lstas_cpr_lpr h o G L T. +#h #o #G #L #T #HT elim (snv_fwd_aaa … HT) -HT +#A #HT @(aaa_ind_fpbg h o … HT) -G -L -T -A +#G #L #T #A #_ #IH -A @and4_intro +[ letin aux ≝ da_cpr_lpr_aux | letin aux ≝ snv_cpr_lpr_aux +| letin aux ≝ snv_lstas_aux | letin aux ≝ lstas_cpr_lpr_aux +] +@(aux … G L T) // #G0 #L0 #T0 #H elim (IH … H) -IH -H // +qed-. + +theorem da_cpr_lpr: ∀h,o,G,L,T. IH_da_cpr_lpr h o G L T. +#h #o #G #L #T #HT elim (snv_preserve … HT) /2 width=1 by/ +qed-. + +theorem snv_cpr_lpr: ∀h,o,G,L,T. IH_snv_cpr_lpr h o G L T. +#h #o #G #L #T #HT elim (snv_preserve … HT) /2 width=1 by/ +qed-. + +theorem snv_lstas: ∀h,o,G,L,T. IH_snv_lstas h o G L T. +#h #o #G #L #T #HT elim (snv_preserve … HT) /2 width=5 by/ +qed-. + +theorem lstas_cpr_lpr: ∀h,o,G,L,T. IH_lstas_cpr_lpr h o G L T. +#h #o #G #L #T #HT elim (snv_preserve … HT) /2 width=3 by/ +qed-. + +(* Advanced preservation properties *****************************************) + +lemma snv_cprs_lpr: ∀h,o,G,L1,T1. ⦃G, L1⦄ ⊢ T1 ¡[h, o] → + ∀T2. ⦃G, L1⦄ ⊢ T1 ➡* T2 → ∀L2. ⦃G, L1⦄ ⊢ ➡ L2 → ⦃G, L2⦄ ⊢ T2 ¡[h, o]. +#h #o #G #L1 #T1 #HT1 #T2 #H +@(cprs_ind … H) -T2 /3 width=5 by snv_cpr_lpr/ +qed-. + +lemma da_cprs_lpr: ∀h,o,G,L1,T1. ⦃G, L1⦄ ⊢ T1 ¡[h, o] → + ∀d. ⦃G, L1⦄ ⊢ T1 ▪[h, o] d → + ∀T2. ⦃G, L1⦄ ⊢ T1 ➡* T2 → ∀L2. ⦃G, L1⦄ ⊢ ➡ L2 → ⦃G, L2⦄ ⊢ T2 ▪[h, o] d. +#h #o #G #L1 #T1 #HT1 #d #Hd #T2 #H +@(cprs_ind … H) -T2 /3 width=6 by snv_cprs_lpr, da_cpr_lpr/ +qed-. + +lemma lstas_cprs_lpr: ∀h,o,G,L1,T1. ⦃G, L1⦄ ⊢ T1 ¡[h, o] → + ∀d1,d2. d2 ≤ d1 → ⦃G, L1⦄ ⊢ T1 ▪[h, o] d1 → + ∀U1. ⦃G, L1⦄ ⊢ T1 •*[h, d2] U1 → + ∀T2. ⦃G, L1⦄ ⊢ T1 ➡* T2 → ∀L2. ⦃G, L1⦄ ⊢ ➡ L2 → + ∃∃U2. ⦃G, L2⦄ ⊢ T2 •*[h, d2] U2 & ⦃G, L2⦄ ⊢ U1 ⬌* U2. +#h #o #G #L1 #T1 #HT1 #d1 #d2 #Hd21 #Hd1 #U1 #HTU1 #T2 #H +@(cprs_ind … H) -T2 [ /2 width=10 by lstas_cpr_lpr/ ] +#T #T2 #HT1T #HTT2 #IHT1 #L2 #HL12 +elim (IHT1 L1) // -IHT1 #U #HTU #HU1 +elim (lstas_cpr_lpr … o … Hd21 … HTU … HTT2 … HL12) -HTU -HTT2 +[2,3: /2 width=7 by snv_cprs_lpr, da_cprs_lpr/ ] -T1 -T -d1 +/4 width=5 by lpr_cpcs_conf, cpcs_trans, ex2_intro/ +qed-. + +lemma lstas_cpcs_lpr: ∀h,o,G,L1,T1. ⦃G, L1⦄ ⊢ T1 ¡[h, o] → + ∀d,d1. d ≤ d1 → ⦃G, L1⦄ ⊢ T1 ▪[h, o] d1 → ∀U1. ⦃G, L1⦄ ⊢ T1 •*[h, d] U1 → + ∀T2. ⦃G, L1⦄ ⊢ T2 ¡[h, o] → + ∀d2. d ≤ d2 → ⦃G, L1⦄ ⊢ T2 ▪[h, o] d2 → ∀U2. ⦃G, L1⦄ ⊢ T2 •*[h, d] U2 → + ⦃G, L1⦄ ⊢ T1 ⬌* T2 → ∀L2. ⦃G, L1⦄ ⊢ ➡ L2 → ⦃G, L2⦄ ⊢ U1 ⬌* U2. +#h #o #G #L1 #T1 #HT1 #d #d1 #Hd1 #HTd1 #U1 #HTU1 #T2 #HT2 #d2 #Hd2 #HTd2 #U2 #HTU2 #H #L2 #HL12 +elim (cpcs_inv_cprs … H) -H #T #H1 #H2 +elim (lstas_cprs_lpr … HT1 … Hd1 HTd1 … HTU1 … H1 … HL12) -T1 #W1 #H1 #HUW1 +elim (lstas_cprs_lpr … HT2 … Hd2 HTd2 … HTU2 … H2 … HL12) -T2 #W2 #H2 #HUW2 +lapply (lstas_mono … H1 … H2) -h -T -d #H destruct /2 width=3 by cpcs_canc_dx/ +qed-. diff --git a/matita/matita/contribs/lambdadelta/basic_2/dynamic/snv_preserve.ma b/matita/matita/contribs/lambdadelta/basic_2/dynamic/snv_preserve.ma deleted file mode 100644 index 482b94451..000000000 --- a/matita/matita/contribs/lambdadelta/basic_2/dynamic/snv_preserve.ma +++ /dev/null @@ -1,94 +0,0 @@ -(**************************************************************************) -(* ___ *) -(* ||M|| *) -(* ||A|| A project by Andrea Asperti *) -(* ||T|| *) -(* ||I|| Developers: *) -(* ||T|| The HELM team. *) -(* ||A|| http://helm.cs.unibo.it *) -(* \ / *) -(* \ / This file is distributed under the terms of the *) -(* v GNU General Public License Version 2 *) -(* *) -(**************************************************************************) - -include "basic_2/computation/fsb_aaa.ma". -include "basic_2/dynamic/snv_da_lpr.ma". -include "basic_2/dynamic/snv_lstas.ma". -include "basic_2/dynamic/snv_lstas_lpr.ma". -include "basic_2/dynamic/snv_lpr.ma". - -(* STRATIFIED NATIVE VALIDITY FOR TERMS *************************************) - -(* Main preservation properties *********************************************) - -lemma snv_preserve: ∀h,o,G,L,T. ⦃G, L⦄ ⊢ T ¡[h, o] → - ∧∧ IH_da_cpr_lpr h o G L T - & IH_snv_cpr_lpr h o G L T - & IH_snv_lstas h o G L T - & IH_lstas_cpr_lpr h o G L T. -#h #o #G #L #T #HT elim (snv_fwd_aaa … HT) -HT -#A #HT @(aaa_ind_fpbg h o … HT) -G -L -T -A -#G #L #T #A #_ #IH -A @and4_intro -[ letin aux ≝ da_cpr_lpr_aux | letin aux ≝ snv_cpr_lpr_aux -| letin aux ≝ snv_lstas_aux | letin aux ≝ lstas_cpr_lpr_aux -] -@(aux … G L T) // #G0 #L0 #T0 #H elim (IH … H) -IH -H // -qed-. - -theorem da_cpr_lpr: ∀h,o,G,L,T. IH_da_cpr_lpr h o G L T. -#h #o #G #L #T #HT elim (snv_preserve … HT) /2 width=1 by/ -qed-. - -theorem snv_cpr_lpr: ∀h,o,G,L,T. IH_snv_cpr_lpr h o G L T. -#h #o #G #L #T #HT elim (snv_preserve … HT) /2 width=1 by/ -qed-. - -theorem snv_lstas: ∀h,o,G,L,T. IH_snv_lstas h o G L T. -#h #o #G #L #T #HT elim (snv_preserve … HT) /2 width=5 by/ -qed-. - -theorem lstas_cpr_lpr: ∀h,o,G,L,T. IH_lstas_cpr_lpr h o G L T. -#h #o #G #L #T #HT elim (snv_preserve … HT) /2 width=3 by/ -qed-. - -(* Advanced preservation properties *****************************************) - -lemma snv_cprs_lpr: ∀h,o,G,L1,T1. ⦃G, L1⦄ ⊢ T1 ¡[h, o] → - ∀T2. ⦃G, L1⦄ ⊢ T1 ➡* T2 → ∀L2. ⦃G, L1⦄ ⊢ ➡ L2 → ⦃G, L2⦄ ⊢ T2 ¡[h, o]. -#h #o #G #L1 #T1 #HT1 #T2 #H -@(cprs_ind … H) -T2 /3 width=5 by snv_cpr_lpr/ -qed-. - -lemma da_cprs_lpr: ∀h,o,G,L1,T1. ⦃G, L1⦄ ⊢ T1 ¡[h, o] → - ∀d. ⦃G, L1⦄ ⊢ T1 ▪[h, o] d → - ∀T2. ⦃G, L1⦄ ⊢ T1 ➡* T2 → ∀L2. ⦃G, L1⦄ ⊢ ➡ L2 → ⦃G, L2⦄ ⊢ T2 ▪[h, o] d. -#h #o #G #L1 #T1 #HT1 #d #Hd #T2 #H -@(cprs_ind … H) -T2 /3 width=6 by snv_cprs_lpr, da_cpr_lpr/ -qed-. - -lemma lstas_cprs_lpr: ∀h,o,G,L1,T1. ⦃G, L1⦄ ⊢ T1 ¡[h, o] → - ∀d1,d2. d2 ≤ d1 → ⦃G, L1⦄ ⊢ T1 ▪[h, o] d1 → - ∀U1. ⦃G, L1⦄ ⊢ T1 •*[h, d2] U1 → - ∀T2. ⦃G, L1⦄ ⊢ T1 ➡* T2 → ∀L2. ⦃G, L1⦄ ⊢ ➡ L2 → - ∃∃U2. ⦃G, L2⦄ ⊢ T2 •*[h, d2] U2 & ⦃G, L2⦄ ⊢ U1 ⬌* U2. -#h #o #G #L1 #T1 #HT1 #d1 #d2 #Hd21 #Hd1 #U1 #HTU1 #T2 #H -@(cprs_ind … H) -T2 [ /2 width=10 by lstas_cpr_lpr/ ] -#T #T2 #HT1T #HTT2 #IHT1 #L2 #HL12 -elim (IHT1 L1) // -IHT1 #U #HTU #HU1 -elim (lstas_cpr_lpr … o … Hd21 … HTU … HTT2 … HL12) -HTU -HTT2 -[2,3: /2 width=7 by snv_cprs_lpr, da_cprs_lpr/ ] -T1 -T -d1 -/4 width=5 by lpr_cpcs_conf, cpcs_trans, ex2_intro/ -qed-. - -lemma lstas_cpcs_lpr: ∀h,o,G,L1,T1. ⦃G, L1⦄ ⊢ T1 ¡[h, o] → - ∀d,d1. d ≤ d1 → ⦃G, L1⦄ ⊢ T1 ▪[h, o] d1 → ∀U1. ⦃G, L1⦄ ⊢ T1 •*[h, d] U1 → - ∀T2. ⦃G, L1⦄ ⊢ T2 ¡[h, o] → - ∀d2. d ≤ d2 → ⦃G, L1⦄ ⊢ T2 ▪[h, o] d2 → ∀U2. ⦃G, L1⦄ ⊢ T2 •*[h, d] U2 → - ⦃G, L1⦄ ⊢ T1 ⬌* T2 → ∀L2. ⦃G, L1⦄ ⊢ ➡ L2 → ⦃G, L2⦄ ⊢ U1 ⬌* U2. -#h #o #G #L1 #T1 #HT1 #d #d1 #Hd1 #HTd1 #U1 #HTU1 #T2 #HT2 #d2 #Hd2 #HTd2 #U2 #HTU2 #H #L2 #HL12 -elim (cpcs_inv_cprs … H) -H #T #H1 #H2 -elim (lstas_cprs_lpr … HT1 … Hd1 HTd1 … HTU1 … H1 … HL12) -T1 #W1 #H1 #HUW1 -elim (lstas_cprs_lpr … HT2 … Hd2 HTd2 … HTU2 … H2 … HL12) -T2 #W2 #H2 #HUW2 -lapply (lstas_mono … H1 … H2) -h -T -d #H destruct /2 width=3 by cpcs_canc_dx/ -qed-. diff --git a/matita/matita/contribs/lambdadelta/basic_2/dynamic/snv_scpes.ma b/matita/matita/contribs/lambdadelta/basic_2/dynamic/snv_scpes.ma deleted file mode 100644 index 61d7fbdea..000000000 --- a/matita/matita/contribs/lambdadelta/basic_2/dynamic/snv_scpes.ma +++ /dev/null @@ -1,198 +0,0 @@ -(**************************************************************************) -(* ___ *) -(* ||M|| *) -(* ||A|| A project by Andrea Asperti *) -(* ||T|| *) -(* ||I|| Developers: *) -(* ||T|| The HELM team. *) -(* ||A|| http://helm.cs.unibo.it *) -(* \ / *) -(* \ / This file is distributed under the terms of the *) -(* v GNU General Public License Version 2 *) -(* *) -(**************************************************************************) - -include "basic_2/computation/fpbg_fpbs.ma". -include "basic_2/equivalence/scpes_cpcs.ma". -include "basic_2/equivalence/scpes_scpes.ma". -include "basic_2/dynamic/snv.ma". - -(* STRATIFIED NATIVE VALIDITY FOR TERMS *************************************) - -(* Inductive premises for the preservation results **************************) - -definition IH_snv_cpr_lpr: ∀h:sh. sd h → relation3 genv lenv term ≝ - λh,o,G,L1,T1. ⦃G, L1⦄ ⊢ T1 ¡[h, o] → - ∀T2. ⦃G, L1⦄ ⊢ T1 ➡ T2 → ∀L2. ⦃G, L1⦄ ⊢ ➡ L2 → ⦃G, L2⦄ ⊢ T2 ¡[h, o]. - -definition IH_da_cpr_lpr: ∀h:sh. sd h → relation3 genv lenv term ≝ - λh,o,G,L1,T1. ⦃G, L1⦄ ⊢ T1 ¡[h, o] → - ∀d. ⦃G, L1⦄ ⊢ T1 ▪[h, o] d → - ∀T2. ⦃G, L1⦄ ⊢ T1 ➡ T2 → ∀L2. ⦃G, L1⦄ ⊢ ➡ L2 → - ⦃G, L2⦄ ⊢ T2 ▪[h, o] d. - -definition IH_lstas_cpr_lpr: ∀h:sh. sd h → relation3 genv lenv term ≝ - λh,o,G,L1,T1. ⦃G, L1⦄ ⊢ T1 ¡[h, o] → - ∀d1,d2. d2 ≤ d1 → ⦃G, L1⦄ ⊢ T1 ▪[h, o] d1 → - ∀U1. ⦃G, L1⦄ ⊢ T1 •*[h, d2] U1 → - ∀T2. ⦃G, L1⦄ ⊢ T1 ➡ T2 → ∀L2. ⦃G, L1⦄ ⊢ ➡ L2 → - ∃∃U2. ⦃G, L2⦄ ⊢ T2 •*[h, d2] U2 & ⦃G, L2⦄ ⊢ U1 ⬌* U2. - -definition IH_snv_lstas: ∀h:sh. sd h → relation3 genv lenv term ≝ - λh,o,G,L,T. ⦃G, L⦄ ⊢ T ¡[h, o] → - ∀d1,d2. d2 ≤ d1 → ⦃G, L⦄ ⊢ T ▪[h, o] d1 → - ∀U. ⦃G, L⦄ ⊢ T •*[h, d2] U → ⦃G, L⦄ ⊢ U ¡[h, o]. - -(* Properties for the preservation results **********************************) - -fact snv_cprs_lpr_aux: ∀h,o,G0,L0,T0. - (∀G1,L1,T1. ⦃G0, L0, T0⦄ >≛[h, o] ⦃G1, L1, T1⦄ → IH_snv_cpr_lpr h o G1 L1 T1) → - ∀G,L1,T1. ⦃G0, L0, T0⦄ >≛[h, o] ⦃G, L1, T1⦄ → ⦃G, L1⦄ ⊢ T1 ¡[h, o] → - ∀T2. ⦃G, L1⦄ ⊢ T1 ➡* T2 → ∀L2. ⦃G, L1⦄ ⊢ ➡ L2 → ⦃G, L2⦄ ⊢ T2 ¡[h, o]. -#h #o #G0 #L0 #T0 #IH #G #L1 #T1 #HLT0 #HT1 #T2 #H -@(cprs_ind … H) -T2 /4 width=6 by fpbg_fpbs_trans, cprs_fpbs/ -qed-. - -fact da_cprs_lpr_aux: ∀h,o,G0,L0,T0. - (∀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) → - ∀G,L1,T1. ⦃G0, L0, T0⦄ >≛[h, o] ⦃G, L1, T1⦄ → ⦃G, L1⦄ ⊢ T1 ¡[h, o] → - ∀d. ⦃G, L1⦄ ⊢ T1 ▪[h, o] d → - ∀T2. ⦃G, L1⦄ ⊢ T1 ➡* T2 → ∀L2. ⦃G, L1⦄ ⊢ ➡ L2 → ⦃G, L2⦄ ⊢ T2 ▪[h, o] d. -#h #o #G0 #L0 #T0 #IH2 #IH1 #G #L1 #T1 #HLT0 #HT1 #d #Hd #T2 #H -@(cprs_ind … H) -T2 /4 width=10 by snv_cprs_lpr_aux, fpbg_fpbs_trans, cprs_fpbs/ -qed-. - -fact da_scpds_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) → - ∀G,L1,T1. ⦃G0, L0, T0⦄ >≛[h, o] ⦃G, L1, T1⦄ → ⦃G, L1⦄ ⊢ T1 ¡[h, o] → - ∀d1. ⦃G, L1⦄ ⊢ T1 ▪[h, o] d1 → - ∀T2,d2. ⦃G, L1⦄ ⊢ T1 •*➡*[h, o, d2] T2 → ∀L2. ⦃G, L1⦄ ⊢ ➡ L2 → - d2 ≤ d1 ∧ ⦃G, L2⦄ ⊢ T2 ▪[h, o] d1-d2. -#h #o #G0 #L0 #T0 #IH3 #IH2 #IH1 #G #L1 #T1 #HLT0 #HT1 #d1 #Hd1 #T2 #d2 * #T #d0 #Hd20 #H #HT1 #HT2 #L2 #HL12 -lapply (da_mono … H … Hd1) -H #H destruct -lapply (lstas_da_conf … HT1 … Hd1) #Hd12 -lapply (da_cprs_lpr_aux … IH2 IH1 … Hd12 … HT2 … HL12) -IH2 -IH1 -HT2 -HL12 -/3 width=8 by fpbg_fpbs_trans, lstas_fpbs, conj/ -qed-. - -fact da_scpes_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) → - ∀G,L,T1. ⦃G0, L0, T0⦄ >≛[h, o] ⦃G, L, T1⦄ → ⦃G, L⦄ ⊢ T1 ¡[h, o] → - ∀T2. ⦃G0, L0, T0⦄ >≛[h, o] ⦃G, L, T2⦄ → ⦃G, L⦄ ⊢ T2 ¡[h, o] → - ∀d11. ⦃G, L⦄ ⊢ T1 ▪[h, o] d11 → ∀d12. ⦃G, L⦄ ⊢ T2 ▪[h, o] d12 → - ∀d21,d22. ⦃G, L⦄ ⊢ T1 •*⬌*[h, o, d21, d22] T2 → - ∧∧ d21 ≤ d11 & d22 ≤ d12 & d11 - d21 = d12 - d22. -#h #o #G0 #L0 #T0 #IH3 #IH2 #IH1 #G #L #T1 #HLT01 #HT1 #T2 #HLT02 #HT2 #d11 #Hd11 #d12 #Hd12 #d21 #d22 * #T #HT1 #HT2 -elim (da_scpds_lpr_aux … IH3 IH2 IH1 … Hd11 … HT1 … L) -Hd11 -HT1 // -elim (da_scpds_lpr_aux … IH3 IH2 IH1 … Hd12 … HT2 … L) -Hd12 -HT2 // -/3 width=7 by da_mono, and3_intro/ -qed-. - -fact lstas_cprs_lpr_aux: ∀h,o,G0,L0,T0. - (∀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) → - ∀G,L1,T1. ⦃G0, L0, T0⦄ >≛[h, o] ⦃G, L1, T1⦄ → ⦃G, L1⦄ ⊢ T1 ¡[h, o] → - ∀d1,d2. d2 ≤ d1 → ⦃G, L1⦄ ⊢ T1 ▪[h, o] d1 → - ∀U1. ⦃G, L1⦄ ⊢ T1 •*[h, d2] U1 → - ∀T2. ⦃G, L1⦄ ⊢ T1 ➡* T2 → ∀L2. ⦃G, L1⦄ ⊢ ➡ L2 → - ∃∃U2. ⦃G, L2⦄ ⊢ T2 •*[h, d2] U2 & ⦃G, L2⦄ ⊢ U1 ⬌* U2. -#h #o #G0 #L0 #T0 #IH3 #IH2 #IH1 #G #L1 #T1 #H01 #HT1 #d1 #d2 #Hd21 #Hd1 #U1 #HTU1 #T2 #H -@(cprs_ind … H) -T2 [ /2 width=10 by/ ] -#T #T2 #HT1T #HTT2 #IHT1 #L2 #HL12 -elim (IHT1 L1) // -IHT1 #U #HTU #HU1 -elim (IH1 … Hd21 … HTU … HTT2 … HL12) -IH1 -HTU -HTT2 -[2: /3 width=12 by da_cprs_lpr_aux/ -|3: /3 width=10 by snv_cprs_lpr_aux/ -|4: /3 width=5 by fpbg_fpbs_trans, cprs_fpbs/ -] -G0 -L0 -T0 -T1 -T -d1 -/4 width=5 by lpr_cpcs_conf, cpcs_trans, ex2_intro/ -qed-. - -fact scpds_cpr_lpr_aux: ∀h,o,G0,L0,T0. - (∀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) → - ∀G,L1,T1. ⦃G0, L0, T0⦄ >≛[h, o] ⦃G, L1, T1⦄ → ⦃G, L1⦄ ⊢ T1 ¡[h, o] → - ∀U1,d. ⦃G, L1⦄ ⊢ T1 •*➡*[h, o, d] U1 → - ∀T2. ⦃G, L1⦄ ⊢ T1 ➡ T2 → ∀L2. ⦃G, L1⦄ ⊢ ➡ L2 → - ∃∃U2. ⦃G, L2⦄ ⊢ T2 •*➡*[h, o, d] U2 & ⦃G, L2⦄ ⊢ U1 ➡* U2. -#h #o #G0 #L0 #T0 #IH2 #IH1 #G #L1 #T1 #H01 #HT1 #U1 #d2 * #W1 #d1 #Hd21 #HTd1 #HTW1 #HWU1 #T2 #HT12 #L2 #HL12 -elim (IH1 … H01 … HTW1 … HT12 … HL12) -IH1 // #W2 #HTW2 #HW12 -lapply (IH2 … H01 … HTd1 … HT12 … HL12) -L0 -T0 // -T1 -lapply (lpr_cprs_conf … HL12 … HWU1) -L1 #HWU1 -lapply (cpcs_canc_sn … HW12 HWU1) -W1 #H -elim (cpcs_inv_cprs … H) -H /3 width=6 by ex4_2_intro, ex2_intro/ -qed-. - -fact scpes_cpr_lpr_aux: ∀h,o,G0,L0,T0. - (∀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) → - ∀G,L1,T1. ⦃G0, L0, T0⦄ >≛[h, o] ⦃G, L1, T1⦄ → ⦃G, L1⦄ ⊢ T1 ¡[h, o] → - ∀T2. ⦃G0, L0, T0⦄ >≛[h, o] ⦃G, L1, T2⦄ → ⦃G, L1⦄ ⊢ T2 ¡[h, o] → - ∀d1,d2. ⦃G, L1⦄ ⊢ T1 •*⬌*[h, o, d1, d2] T2 → - ∀U1. ⦃G, L1⦄ ⊢ T1 ➡ U1 → ∀U2. ⦃G, L1⦄ ⊢ T2 ➡ U2 → ∀L2. ⦃G, L1⦄ ⊢ ➡ L2 → - ⦃G, L2⦄ ⊢ U1 •*⬌*[h, o, d1, d2] U2. -#h #o #G0 #L0 #T0 #IH2 #IH1 #G #L1 #T1 #H01 #HT1 #T2 #HT02 #HT2 #d1 #d2 * #T0 #HT10 #HT20 #U1 #HTU1 #U2 #HTU2 #L2 #HL12 -elim (scpds_cpr_lpr_aux … IH2 IH1 … HT10 … HTU1 … HL12) -HT10 -HTU1 // #X1 #HUX1 #H1 -elim (scpds_cpr_lpr_aux … IH2 IH1 … HT20 … HTU2 … HL12) -HT20 -HTU2 // #X2 #HUX2 #H2 -elim (cprs_conf … H1 … H2) -T0 -/3 width=5 by scpds_div, scpds_cprs_trans/ -qed-. - -fact lstas_scpds_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) → - ∀G,L,T. ⦃G0, L0, T0⦄ >≛[h, o] ⦃G, L, T⦄ → ⦃G, L⦄ ⊢ T ¡[h, o] → - ∀d,d1. d1 ≤ d → ⦃G, L⦄ ⊢ T ▪[h, o] d → ∀T1. ⦃G, L⦄ ⊢ T •*[h, d1] T1 → - ∀T2,d2. ⦃G, L⦄ ⊢ T •*➡*[h, o, d2] T2 → ⦃G, L⦄ ⊢ T1 •*⬌*[h, o, d2-d1, d1-d2] T2. -#h #o #G0 #L0 #T0 #IH4 #IH3 #IH2 #IH1 #G #L #T #H0 #HT #d #d1 #Hd1 #HTd #T1 #HT1 #T2 #d2 * #X #d0 #Hd20 #H #HTX #HXT2 -lapply (da_mono … H … HTd) -H #H destruct -lapply (lstas_da_conf … HT1 … HTd) #HTd1 -lapply (lstas_da_conf … HTX … HTd) #HXd -lapply (da_cprs_lpr_aux … IH3 IH2 … HXd … HXT2 L ?) -[1,2,3: /3 width=8 by fpbg_fpbs_trans, lstas_fpbs/ ] #HTd2 -elim (le_or_ge d1 d2) #Hd12 >(eq_minus_O … Hd12) -[ elim (da_lstas … HTd2 0) #X2 #HTX2 #_ -IH4 -IH3 -IH2 -IH1 -H0 -HT -HTd -HXd - /5 width=6 by lstas_scpds, scpds_div, cprs_strap1, lstas_cpr, lstas_conf_le, monotonic_le_minus_l, ex4_2_intro/ -| elim (da_lstas … HTd1 0) #X1 #HTX1 #_ - lapply (lstas_conf_le … HTX … HT1) // #HXT1 -HT1 - elim (lstas_cprs_lpr_aux … IH3 IH2 IH1 … HXd … HXT1 … HXT2 L) -IH3 -IH2 -IH1 -HXd -HXT1 -HXT2 - /4 width=8 by cpcs_scpes, cpcs_cpr_conf, fpbg_fpbs_trans, lstas_fpbs, lstas_cpr, monotonic_le_minus_l/ -] -qed-. - -fact scpes_le_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) → - ∀G,L,T1. ⦃G0, L0, T0⦄ >≛[h, o] ⦃G, L, T1⦄ → ⦃G, L⦄ ⊢ T1 ¡[h, o] → - ∀T2. ⦃G0, L0, T0⦄ >≛[h, o] ⦃G, L, T2⦄ → ⦃G, L⦄ ⊢ T2 ¡[h, o] → - ∀d11. ⦃G, L⦄ ⊢ T1 ▪[h, o] d11 → ∀d12. ⦃G, L⦄ ⊢ T2 ▪[h, o] d12 → - ∀d21,d22,d. d21 + d ≤ d11 → d22 + d ≤ d12 → - ⦃G, L⦄ ⊢ T1 •*⬌*[h, o, d21, d22] T2 → ⦃G, L⦄ ⊢ T1 •*⬌*[h, o, d21+d, d22+d] T2. -#h #o #G0 #L0 #T0 #IH4 #IH3 #IH2 #IH1 #G #L #T1 #H01 #HT1 #T2 #H02 #HT2 #d11 #Hd11 #Hd12 #Hd12 #d21 #d22 #d #H1 #H2 * #T0 #HT10 #HT20 -elim (da_lstas … Hd11 (d21+d)) #X1 #HTX1 #_ -elim (da_lstas … Hd12 (d22+d)) #X2 #HTX2 #_ -lapply (lstas_scpds_aux … IH4 IH3 IH2 IH1 … Hd11 … HTX1 … HT10) -HT10 -[1,2,3: // | >eq_minus_O [2: // ] eq_minus_O [2: // ] plus_S1 + /3 width=11 by cpm_lifts_bi, cpms_step_dx/ +] +qed. + (* Advanced inversion lemmas ************************************************) lemma cpms_inv_lref1_drops (n) (h) (G): diff --git a/matita/matita/contribs/lambdadelta/basic_2/web/basic_2_src.tbl b/matita/matita/contribs/lambdadelta/basic_2/web/basic_2_src.tbl index 32063da4b..143c8ccb1 100644 --- a/matita/matita/contribs/lambdadelta/basic_2/web/basic_2_src.tbl +++ b/matita/matita/contribs/lambdadelta/basic_2/web/basic_2_src.tbl @@ -31,7 +31,7 @@ table { *) [ { "context-sensitive native validity" * } { [ [ "restricted refinement for lenvs" ] "lsubv ( ? ⊢ ? ⫃![?,?] ? )" "lsubv_drops" + "lsubv_lsubr" + "lsubv_lsuba" + "lsubv_cpms" + "lsubv_cpcs" + "lsubv_cnv" + "lsubv_lsubv" * ] - [ [ "for terms" ] "cnv" + "( ⦃?,?⦄ ⊢ ? ![?,?] )" "cnv_drops" + "cnv_fqus" + "cnv_aaa" + "cnv_fsb" + "cnv_cpm_trans" (* + "cnv_scpes" + "cnv_preserve" *) * ] + [ [ "for terms" ] "cnv" + "( ⦃?,?⦄ ⊢ ? ![?,?] )" "cnv_drops" + "cnv_fqus" + "cnv_aaa" + "cnv_fsb" + "cnv_cpm_trans" + "cnv_cpm_conf" + "cnv_preserve_far" (* + "cnv_preserve" *) * ] } ] } diff --git a/matita/matita/contribs/lambdadelta/compile_partial.sh b/matita/matita/contribs/lambdadelta/compile_partial.sh index d5789f4b8..817d68bc0 100644 --- a/matita/matita/contribs/lambdadelta/compile_partial.sh +++ b/matita/matita/contribs/lambdadelta/compile_partial.sh @@ -1,4 +1 @@ ../../matitac.opt `cat partial.txt` -cd basic_2/dynamic/ -../../../../matitac.opt `cat partial.txt` -cd ../../ diff --git a/matita/matita/contribs/lambdadelta/ground_2/lib/arith.ma b/matita/matita/contribs/lambdadelta/ground_2/lib/arith.ma index e3ec5c504..dfc61de15 100644 --- a/matita/matita/contribs/lambdadelta/ground_2/lib/arith.ma +++ b/matita/matita/contribs/lambdadelta/ground_2/lib/arith.ma @@ -60,9 +60,11 @@ lemma minus_plus_m_m_commutative: ∀n,m:nat. n = m + n - m. lemma plus_n_2: ∀n. n + 2 = n + 1 + 1. // qed. -lemma arith_l: ∀x. 1 = 1-x+(x-(x-1)). -* // #x >minus_S_S >minus_S_S