From: Ferruccio Guidi Date: Mon, 13 May 2013 21:23:25 +0000 (+0000) Subject: partial commit of the "dynamic" component X-Git-Tag: make_still_working~1155 X-Git-Url: http://matita.cs.unibo.it/gitweb/?a=commitdiff_plain;h=211b0c8d77c4cebba7a629601038d0f5fd76c250;p=helm.git partial commit of the "dynamic" component --- diff --git a/matita/matita/contribs/lambdadelta/basic_2/computation/cprs_lpss.ma b/matita/matita/contribs/lambdadelta/basic_2/computation/cprs_lpss.ma index 4aedee56d..271094919 100644 --- a/matita/matita/contribs/lambdadelta/basic_2/computation/cprs_lpss.ma +++ b/matita/matita/contribs/lambdadelta/basic_2/computation/cprs_lpss.ma @@ -12,7 +12,7 @@ (* *) (**************************************************************************) -include "basic_2/substitution/lpss_cpss.ma". +include "basic_2/substitution/lpss_lpss.ma". include "basic_2/reduction/lpr_lpss.ma". include "basic_2/computation/cprs.ma". @@ -47,3 +47,46 @@ lemma cprs_lpss_conf_sn: ∀L0,T0,T1. L0 ⊢ T0 ➡* T1 → ∀L1. L0 ⊢ ▶* L elim (cprs_lpss_conf_dx … HT01 … HL01) -HT01 #T #HT1 lapply (lpss_cpss_trans … HL01 … HT1) -HT1 /2 width=3/ qed-. + +lemma cprs_cpss_lpss_conf_sn: ∀L1,T1,U1. L1 ⊢ T1 ➡* U1 → + ∀T2. L1 ⊢ T1 ▶* T2 → ∀L2. L1 ⊢ ▶* L2 → + ∃∃U2. L2 ⊢ T2 ➡* U2 & L1 ⊢ U1 ▶* U2. +#L1 #T1 #U1 #HTU1 #T2 #HT12 #L2 #HL12 +elim (cprs_cpss_conf … HTU1 … HT12) -T1 #U #HU1 #HT2U +elim (cprs_lpss_conf_sn … HT2U … HL12) -HT2U -HL12 #U2 #HU2 #HTU2 +lapply (cpss_trans … HU1 … HU2) -U /2 width=3/ +qed-. + +lemma cprs_cpss_lpss_conf_dx: ∀L1,T1,U1. L1 ⊢ T1 ➡* U1 → + ∀T2. L1 ⊢ T1 ▶* T2 → ∀L2. L1 ⊢ ▶* L2 → + ∃∃U2. L2 ⊢ T2 ➡* U2 & L2 ⊢ U1 ▶* U2. +#L1 #T1 #U1 #HTU1 #T2 #HT12 #L2 #HL12 +elim (cprs_lpss_conf_dx … HTU1 … HL12) -HTU1 #U2 #HU12 #HT1U2 +elim (lpss_cpss_conf_dx … HT12 … HL12) -L1 #T #HT1 #HT2 +elim (cprs_cpss_conf … HT1U2 … HT1) -T1 #U #HU2 #HTU +lapply (cpss_trans … HU12 … HU2) -U2 +lapply (cpss_cprs_trans … HT2 … HTU) -T /2 width=3/ +qed-. + + +lemma cprs_cpss2_lpss_conf_sn: ∀L1,T1,U1. L1 ⊢ T1 ➡* U1 → ∀T2. L1 ⊢ T1 ▶* T2 → + ∀U2. L1 ⊢ U1 ▶* U2 → ∀L2. L1 ⊢ ▶* L2 → + ∃∃U. L2 ⊢ T2 ➡* U & L1 ⊢ U2 ▶* U. +#L1 #T1 #U1 #HTU1 #T2 #HT12 #U2 #HU12 #L2 #HL12 +elim (cprs_cpss_lpss_conf_sn … HTU1 … HT12 … HL12) -T1 #T1 #HT21 #HUT1 +elim (cpss_conf … HU12 … HUT1) -U1 #U1 #HU21 #HTU1 +elim (lpss_cpss_conf_sn … HTU1 … HL12) -HTU1 -HL12 #U2 #HT1U2 #HU12 +lapply (cpss_trans … HU21 … HU12) -U1 +lapply (cprs_cpss_trans … HT21 … HT1U2) -T1 /2 width=3/ +qed-. + +lemma cprs_cpss2_lpss_conf_dx: ∀L1,T1,U1. L1 ⊢ T1 ➡* U1 → ∀T2. L1 ⊢ T1 ▶* T2 → + ∀U2. L1 ⊢ U1 ▶* U2 → ∀L2. L1 ⊢ ▶* L2 → + ∃∃U. L2 ⊢ T2 ➡* U & L2 ⊢ U2 ▶* U. +#L1 #T1 #U1 #HTU1 #T2 #HT12 #U2 #HU12 #L2 #HL12 +elim (cprs_cpss_lpss_conf_dx … HTU1 … HT12 … HL12) -T1 #T1 #HT21 #HUT1 +elim (lpss_cpss_conf_dx … HU12 … HL12) -L1 #U #HU1 #HU2 +elim (cpss_conf … HU1 … HUT1) -U1 #U1 #HU1 #HTU1 +lapply (cpss_trans … HU2 … HU1) -U +lapply (cprs_cpss_trans … HT21 … HTU1) -T1 /2 width=3/ +qed-. \ No newline at end of file diff --git a/matita/matita/contribs/lambdadelta/basic_2/computation/dxprs_lpss.ma b/matita/matita/contribs/lambdadelta/basic_2/computation/dxprs_lpss.ma index 4b1ce0785..a14c5518b 100644 --- a/matita/matita/contribs/lambdadelta/basic_2/computation/dxprs_lpss.ma +++ b/matita/matita/contribs/lambdadelta/basic_2/computation/dxprs_lpss.ma @@ -32,14 +32,14 @@ qed-. lemma dxprs_cpss_conf: ∀h,g,L,T1,U1. ⦃h, L⦄ ⊢ T1 •*➡*[g] U1 → ∀T2. L ⊢ T1 ▶* T2 → ∃∃U2. ⦃h, L⦄ ⊢ T2 •*➡*[g] U2 & L ⊢ U1 ▶* U2. #h #g #L #T1 #U1 * #W1 #HTW1 #HWU1 #T2 #HT12 -elim (sstas_tpss_conf … HTW1 … HT12) -T1 #W2 #HTW2 #HW12 +elim (sstas_cpss_conf … HTW1 … HT12) -T1 #W2 #HTW2 #HW12 elim (cprs_cpss_conf … HWU1 … HW12) -W1 /3 width=3/ qed-. -lemma dxprs_lpss_cpss_conf: ∀h,g,L1,T1,U1. ⦃h, L1⦄ ⊢ T1 •*➡*[g] U1 → - ∀L2. L1 ⊢ ▶* L2 → ∀T2. L1 ⊢ T1 ▶* T2 → +lemma dxprs_cpss_lpss_conf: ∀h,g,L1,T1,U1. ⦃h, L1⦄ ⊢ T1 •*➡*[g] U1 → + ∀T2. L1 ⊢ T1 ▶* T2 → ∀L2. L1 ⊢ ▶* L2 → ∃∃U2. ⦃h, L2⦄ ⊢ T2 •*➡*[g] U2 & L1 ⊢ U1 ▶* U2. -#h #g #L1 #T1 #U1 #HTU1 #L2 #HL12 #T2 #HT12 +#h #g #L1 #T1 #U1 #HTU1 #T2 #HT12 #L2 #HL12 elim (dxprs_cpss_conf … HTU1 … HT12) -T1 #U2 #HTU2 #HU12 elim (dxprs_lpss_conf … HTU2 … HL12) -HTU2 -HL12 #U #HT2U #HU2 lapply (cpss_trans … HU12 … HU2) -U2 /2 width=3/ diff --git a/matita/matita/contribs/lambdadelta/basic_2/dynamic/lsubsv.ma b/matita/matita/contribs/lambdadelta/basic_2/dynamic/lsubsv.ma index fe0359314..d203f0da4 100644 --- a/matita/matita/contribs/lambdadelta/basic_2/dynamic/lsubsv.ma +++ b/matita/matita/contribs/lambdadelta/basic_2/dynamic/lsubsv.ma @@ -101,11 +101,11 @@ lemma lsubsv_fwd_lsubss: ∀h,g,L1,L2. h ⊢ L1 ¡⊑[g] L2 → h ⊢ L1 •⊑[ #h #g #L1 #L2 #H elim H -L1 -L2 // /2 width=1/ /2 width=6/ qed-. -lemma lsubsv_fwd_lsubr1: ∀h,g,L1,L2. h ⊢ L1 ¡⊑[g] L2 → L1 ⊑[0, |L1|] L2. +lemma lsubsv_fwd_lsubr1: ∀h,g,L1,L2. h ⊢ L1 ¡⊑[g] L2 → L1 ⊑ L2. /3 width=3 by lsubsv_fwd_lsubss, lsubss_fwd_lsubr1/ qed-. -lemma lsubsv_fwd_lsubr2: ∀h,g,L1,L2. h ⊢ L1 ¡⊑[g] L2 → L1 ⊑[0, |L2|] L2. +lemma lsubsv_fwd_lsubr2: ∀h,g,L1,L2. h ⊢ L1 ¡⊑[g] L2 → L1 ⊑ L2. /3 width=3 by lsubsv_fwd_lsubss, lsubss_fwd_lsubr2/ qed-. diff --git a/matita/matita/contribs/lambdadelta/basic_2/dynamic/snv_cpcs.ma b/matita/matita/contribs/lambdadelta/basic_2/dynamic/snv_cpcs.ma index 9451e34d2..643bf6569 100644 --- a/matita/matita/contribs/lambdadelta/basic_2/dynamic/snv_cpcs.ma +++ b/matita/matita/contribs/lambdadelta/basic_2/dynamic/snv_cpcs.ma @@ -12,9 +12,8 @@ (* *) (**************************************************************************) -include "basic_2/unwind/sstas_sstas.ma". -include "basic_2/equivalence/cpcs_ltpr.ma". -include "basic_2/dynamic/snv_ltpss_dx.ma". +include "basic_2/unfold/sstas_sstas.ma". +include "basic_2/equivalence/cpcs_cpcs.ma". include "basic_2/dynamic/snv_sstas.ma". include "basic_2/dynamic/ygt.ma". @@ -22,15 +21,15 @@ include "basic_2/dynamic/ygt.ma". (* Inductive premises for the preservation results **************************) -definition IH_snv_ltpr_tpr: ∀h:sh. sd h → relation2 lenv term ≝ - λh,g,L1,T1. ⦃h, L1⦄ ⊢ T1 ¡[g] → - ∀L2. L1 ➡ L2 → ∀T2. T1 ➡ T2 → ⦃h, L2⦄ ⊢ T2 ¡[g]. +definition IH_snv_cpr_lpr: ∀h:sh. sd h → relation2 lenv term ≝ + λh,g,L1,T1. ⦃h, L1⦄ ⊢ T1 ¡[g] → + ∀T2. L1 ⊢ T1 ➡ T2 → ∀L2. L1 ⊢ ➡ L2 → ⦃h, L2⦄ ⊢ T2 ¡[g]. -definition IH_ssta_ltpr_tpr: ∀h:sh. sd h → relation2 lenv term ≝ - λh,g,L1,T1. ⦃h, L1⦄ ⊢ T1 ¡[g] → - ∀U1,l. ⦃h, L1⦄ ⊢ T1 •[g] ⦃l, U1⦄ → - ∀L2. L1 ➡ L2 → ∀T2. T1 ➡ T2 → - ∃∃U2. ⦃h, L2⦄ ⊢ T2 •[g] ⦃l, U2⦄ & L2 ⊢ U1 ⬌* U2. +definition IH_ssta_cpr_lpr: ∀h:sh. sd h → relation2 lenv term ≝ + λh,g,L1,T1. ⦃h, L1⦄ ⊢ T1 ¡[g] → + ∀U1,l. ⦃h, L1⦄ ⊢ T1 •[g] ⦃l, U1⦄ → + ∀T2. L1 ⊢ T1 ➡ T2 → ∀L2. L1 ⊢ ➡ L2 → + ∃∃U2. ⦃h, L2⦄ ⊢ T2 •[g] ⦃l, U2⦄ & L1 ⊢ U1 ⬌* U2. definition IH_snv_ssta: ∀h:sh. sd h → relation2 lenv term ≝ λh,g,L1,T1. ⦃h, L1⦄ ⊢ T1 ¡[g] → @@ -42,64 +41,45 @@ definition IH_snv_lsubsv: ∀h:sh. sd h → relation2 lenv term ≝ (* Properties for the preservation results **********************************) -fact snv_ltpr_cpr_aux: ∀h,g,L1,T1. IH_snv_ltpr_tpr h g L1 T1 → - ⦃h, L1⦄ ⊢ T1 ¡[g] → - ∀L2. L1 ➡ L2 → ∀T2. L2 ⊢ T1 ➡ T2 → ⦃h, L2⦄ ⊢ T2 ¡[g]. -#h #g #L1 #T1 #IH #HT1 #L2 #HL12 #T2 * #T #HT1T #HTT2 -lapply (IH … HL12 … HT1T) -HL12 // -T1 #HT0 -lapply (snv_tpss_conf … HT0 … HTT2) -T // +fact snv_cprs_lpr_aux: ∀h,g,L0,T0. + (∀L1,T1. h ⊢ ⦃L0, T0⦄ >[g] ⦃L1, T1⦄ → IH_snv_cpr_lpr h g L1 T1) → + ∀L1,T1. h ⊢ ⦃L0, T0⦄ >[g] ⦃L1, T1⦄ → ⦃h, L1⦄ ⊢ T1 ¡[g] → + ∀T2. L1 ⊢ T1 ➡* T2 → ∀L2. L1 ⊢ ➡ L2 → ⦃h, L2⦄ ⊢ T2 ¡[g]. +#h #g #L0 #T0 #IH #L1 #T1 #HLT0 #HT1 #T2 #H +elim H -T2 [ /2 width=6/ ] -HT1 +/4 width=6 by ygt_yprs_trans, cprs_yprs/ qed-. -fact ssta_ltpr_cpr_aux: ∀h,g,L1,T1. IH_ssta_ltpr_tpr h g L1 T1 → - ⦃h, L1⦄ ⊢ T1 ¡[g] → - ∀U1,l. ⦃h, L1⦄ ⊢ T1 •[g] ⦃l, U1⦄ → - ∀L2. L1 ➡ L2 → ∀T2. L2 ⊢ T1 ➡ T2 → - ∃∃U2. ⦃h, L2⦄ ⊢ T2 •[g] ⦃l, U2⦄ & L2 ⊢ U1 ⬌* U2. -#h #g #L1 #T1 #IH #HT1 #U1 #l #HTU1 #L2 #HL12 #T2 * #T #HT1T #HTT2 -elim (IH … HTU1 … HL12 … HT1T) // -L1 -T1 #U #HTU #HU1 -elim (ssta_tpss_conf … HTU … HTT2) -T #U2 #HTU2 #HU2 -lapply (cpcs_cpr_strap1 … HU1 U2 ?) /2 width=3/ -qed-. - -fact snv_ltpr_cprs_aux: ∀h,g,L0,T0. - (∀L1,T1. h ⊢ ⦃L0, T0⦄ >[g] ⦃L1, T1⦄ → IH_snv_ltpr_tpr h g L1 T1) → +fact ssta_cprs_lpr_aux: ∀h,g,L0,T0. + (∀L1,T1. h ⊢ ⦃L0, T0⦄ >[g] ⦃L1, T1⦄ → IH_snv_cpr_lpr h g L1 T1) → + (∀L1,T1. h ⊢ ⦃L0, T0⦄ >[g] ⦃L1, T1⦄ → IH_ssta_cpr_lpr h g L1 T1) → ∀L1,T1. h ⊢ ⦃L0, T0⦄ >[g] ⦃L1, T1⦄ → ⦃h, L1⦄ ⊢ T1 ¡[g] → - ∀L2. L1 ➡ L2 → ∀T2. L2 ⊢ T1 ➡* T2 → ⦃h, L2⦄ ⊢ T2 ¡[g]. -#h #g #L0 #T0 #IH #L1 #T1 #HLT0 #HT1 #L2 #HL12 #T2 #H -@(cprs_ind … H) -T2 [ /2 width=6 by snv_ltpr_cpr_aux/ ] -HT1 -/5 width=6 by snv_ltpr_cpr_aux, ygt_yprs_trans, ltpr_cprs_yprs/ -qed-. - -fact ssta_ltpr_cprs_aux: ∀h,g,L0,T0. - (∀L1,T1. h ⊢ ⦃L0, T0⦄ >[g] ⦃L1, T1⦄ → IH_snv_ltpr_tpr h g L1 T1) → - (∀L1,T1. h ⊢ ⦃L0, T0⦄ >[g] ⦃L1, T1⦄ → IH_ssta_ltpr_tpr h g L1 T1) → - ∀L1,T1. h ⊢ ⦃L0, T0⦄ >[g] ⦃L1, T1⦄ → ⦃h, L1⦄ ⊢ T1 ¡[g] → - ∀U1,l. ⦃h, L1⦄ ⊢ T1 •[g] ⦃l, U1⦄ → - ∀L2. L1 ➡ L2 → ∀T2. L2 ⊢ T1 ➡* T2 → - ∃∃U2. ⦃h, L2⦄ ⊢ T2 •[g] ⦃l, U2⦄ & L2 ⊢ U1 ⬌* U2. -#h #g #L0 #T0 #IH2 #IH1 #L1 #T1 #H01 #HT1 #U1 #l #HTU1 #L2 #HL12 #T2 #H -@(cprs_ind … H) -T2 [ /2 width=7 by ssta_ltpr_cpr_aux/ ] -#T #T2 #HT1T #HTT2 * #U #HTU #HU1 -elim (ssta_ltpr_cpr_aux … HTU … HTT2) // -[2: /3 width=9 by snv_ltpr_cprs_aux/ -|3: /5 width=6 by ygt_yprs_trans, ltpr_cprs_yprs/ -] -L0 -L1 -T0 -T1 -T #U2 #HTU2 #HU2 + ∀U1,l. ⦃h, L1⦄ ⊢ T1 •[g] ⦃l, U1⦄ → + ∀T2. L1 ⊢ T1 ➡* T2 → ∀L2. L1 ⊢ ➡ L2 → + ∃∃U2. ⦃h, L2⦄ ⊢ T2 •[g] ⦃l, U2⦄ & L1 ⊢ U1 ⬌* U2. +#h #g #L0 #T0 #IH2 #IH1 #L1 #T1 #H01 #HT1 #U1 #l #HTU1 #T2 #H +elim H -T2 [ /2 width=5/ ] +#T #T2 #HT1T #HTT2 #IHT1 #L2 #HL12 +elim (IHT1 L1) // -IHT1 #U #HTU #HU1 +elim (IH1 … HTU … HTT2 … HL12) -IH1 -HTU -HTT2 -HL12 +[2: /3 width=9 by snv_cprs_lpr_aux/ +|3: /5 width=6 by ygt_yprs_trans, cprs_yprs/ +] -L0 -T0 -T1 -T #U2 #HTU2 #HU2 lapply (cpcs_trans … HU1 … HU2) -U /2 width=3/ qed-. -fact ssta_ltpr_cpcs_aux: ∀h,g,L0,T0. - (∀L1,T1. h ⊢ ⦃L0, T0⦄ >[g] ⦃L1, T1⦄ → IH_snv_ltpr_tpr h g L1 T1) → - (∀L1,T1. h ⊢ ⦃L0, T0⦄ >[g] ⦃L1, T1⦄ → IH_ssta_ltpr_tpr h g L1 T1) → - ∀L1,L2,T1,T2. h ⊢ ⦃L0, T0⦄ >[g] ⦃L1, T1⦄ → h ⊢ ⦃L0, T0⦄ >[g] ⦃L2, T2⦄ → - ⦃h, L1⦄ ⊢ T1 ¡[g] → ⦃h, L2⦄ ⊢ T2 ¡[g] → - ∀U1,l1. ⦃h, L1⦄ ⊢ T1 •[g] ⦃l1, U1⦄ → - ∀U2,l2. ⦃h, L2⦄ ⊢ T2 •[g] ⦃l2, U2⦄ → - L1 ➡ L2 → L2 ⊢ T1 ⬌* T2 → - l1 = l2 ∧ L2 ⊢ U1 ⬌* U2. -#h #g #L0 #T0 #IH2 #IH1 #L1 #L2 #T1 #T2 #HLT01 #HLT02 #HT1 #HT2 #U1 #l1 #HTU1 #U2 #l2 #HTU2 #HL12 #H +fact ssta_cpcs_aux: ∀h,g,L0,T0. + (∀L1,T1. h ⊢ ⦃L0, T0⦄ >[g] ⦃L1, T1⦄ → IH_snv_cpr_lpr h g L1 T1) → + (∀L1,T1. h ⊢ ⦃L0, T0⦄ >[g] ⦃L1, T1⦄ → IH_ssta_cpr_lpr h g L1 T1) → + ∀L,T1,T2. h ⊢ ⦃L0, T0⦄ >[g] ⦃L, T1⦄ → h ⊢ ⦃L0, T0⦄ >[g] ⦃L, T2⦄ → + ⦃h, L⦄ ⊢ T1 ¡[g] → ⦃h, L⦄ ⊢ T2 ¡[g] → + ∀U1,l1. ⦃h, L⦄ ⊢ T1 •[g] ⦃l1, U1⦄ → + ∀U2,l2. ⦃h, L⦄ ⊢ T2 •[g] ⦃l2, U2⦄ → + L ⊢ T1 ⬌* T2 → l1 = l2 ∧ L ⊢ U1 ⬌* U2. +#h #g #L0 #T0 #IH2 #IH1 #L #T1 #T2 #HLT01 #HLT02 #HT1 #HT2 #U1 #l1 #HTU1 #U2 #l2 #HTU2 #H elim (cpcs_inv_cprs … H) -H #T #H1 #H2 -elim (ssta_ltpr_cprs_aux … HLT01 HT1 … HTU1 … H1) -T1 /2 width=1/ #W1 #H1 #HUW1 -elim (ssta_ltpr_cprs_aux … HLT02 HT2 … HTU2 … H2) -T2 /2 width=1/ #W2 #H2 #HUW2 -L1 -L0 -T0 +elim (ssta_cprs_lpr_aux … HLT01 HT1 … HTU1 … H1 L) -T1 // /2 width=1/ #W1 #H1 #HUW1 +elim (ssta_cprs_lpr_aux … HLT02 HT2 … HTU2 … H2 L) -T2 // /2 width=1/ #W2 #H2 #HUW2 -L0 -T0 elim (ssta_mono … H1 … H2) -h -T #H1 #H2 destruct lapply (cpcs_canc_dx … HUW1 … HUW2) -W2 /2 width=1/ qed-. @@ -112,13 +92,13 @@ fact snv_sstas_aux: ∀h,g,L0,T0. @(sstas_ind … H) -U1 // -HT1 /4 width=5 by ygt_yprs_trans, sstas_yprs/ qed-. -fact sstas_ltpr_cprs_aux: ∀h,g,L0,T0. - (∀L1,T1. h ⊢ ⦃L0, T0⦄ >[g] ⦃L1, T1⦄ → IH_snv_ssta h g L1 T1) → - (∀L1,T1. h ⊢ ⦃L0, T0⦄ >[g] ⦃L1, T1⦄ → IH_snv_ltpr_tpr h g L1 T1) → - (∀L1,T1. h ⊢ ⦃L0, T0⦄ >[g] ⦃L1, T1⦄ → IH_ssta_ltpr_tpr h g L1 T1) → - ∀L1,T1. h ⊢ ⦃L0, T0⦄ >[g] ⦃L1, T1⦄ → ⦃h, L1⦄ ⊢ T1 ¡[g] → - ∀L2. L1 ➡ L2 → ∀T2. L2 ⊢ T1 ➡* T2 → ∀U1. ⦃h, L1⦄ ⊢ T1 •*[g] U1 → - ∃∃U2. ⦃h, L2⦄ ⊢ T2 •*[g] U2 & L2 ⊢ U1 ⬌* U2. +fact sstas_cprs_lpr_aux: ∀h,g,L0,T0. + (∀L1,T1. h ⊢ ⦃L0, T0⦄ >[g] ⦃L1, T1⦄ → IH_snv_ssta h g L1 T1) → + (∀L1,T1. h ⊢ ⦃L0, T0⦄ >[g] ⦃L1, T1⦄ → IH_snv_cpr_lpr h g L1 T1) → + (∀L1,T1. h ⊢ ⦃L0, T0⦄ >[g] ⦃L1, T1⦄ → IH_ssta_cpr_lpr h g L1 T1) → + ∀L1,T1. h ⊢ ⦃L0, T0⦄ >[g] ⦃L1, T1⦄ → ⦃h, L1⦄ ⊢ T1 ¡[g] → + ∀T2. L1 ⊢ T1 ➡* T2 → ∀U1. ⦃h, L1⦄ ⊢ T1 •*[g] U1 → ∀L2. L1 ⊢ ➡ L2 → + ∃∃U2. ⦃h, L2⦄ ⊢ T2 •*[g] U2 & L1 ⊢ U1 ⬌* U2. #h #g #L0 #T0 #IH3 #IH2 #IH1 #L1 #T1 #H01 #HT1 #L2 #HL12 #T2 #HT12 #U1 #H @(sstas_ind … H) -U1 [ /3 width=3/ ] #U1 #W1 #l1 #HTU1 #HUW1 * #U2 #HTU2 #HU12 diff --git a/matita/matita/contribs/lambdadelta/basic_2/dynamic/snv_lift.ma b/matita/matita/contribs/lambdadelta/basic_2/dynamic/snv_lift.ma index e40d8a282..966760b80 100644 --- a/matita/matita/contribs/lambdadelta/basic_2/dynamic/snv_lift.ma +++ b/matita/matita/contribs/lambdadelta/basic_2/dynamic/snv_lift.ma @@ -67,7 +67,7 @@ lemma snv_inv_lift: ∀h,g,L,U. ⦃h, L⦄ ⊢ U ¡[g] → ∀K,d,e. ⇩[d, e] L | #a #L #W #W0 #W1 #U #U1 #l #_ #_ #HW0 #HW01 #HU1 #IHW #IHU #K #d #e #HLK #X #H elim (lift_inv_flat2 … H) -H #V #T #HVW #HTU #H destruct elim (ssta_inv_lift1 … HW0 … HLK … HVW) -HW0 #V0 #HV0 #HVW0 - elim (cprs_inv_lift1 … HLK … HVW0 … HW01) -W0 #V1 #HVW1 #HV01 + elim (cprs_inv_lift1 … HW01 … HLK … HVW0) -W0 #V1 #HVW1 #HV01 elim (dxprs_inv_lift1 … HLK … HTU … HU1) -HU1 #X #H #HTU elim (lift_inv_bind2 … H) -H #Y #T1 #HY #HTU1 #H destruct lapply (lift_inj … HY … HVW1) -HY #H destruct /3 width=8/ diff --git a/matita/matita/contribs/lambdadelta/basic_2/dynamic/snv_lpss.ma b/matita/matita/contribs/lambdadelta/basic_2/dynamic/snv_lpss.ma new file mode 100644 index 000000000..91d34b132 --- /dev/null +++ b/matita/matita/contribs/lambdadelta/basic_2/dynamic/snv_lpss.ma @@ -0,0 +1,73 @@ +(**************************************************************************) +(* ___ *) +(* ||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/dxprs_lpss.ma". +include "basic_2/equivalence/cpcs_lpss.ma". +include "basic_2/dynamic/snv_lift.ma". + +(* STRATIFIED NATIVE VALIDITY FOR TERMS *************************************) + +(* Properties about sn parallel substitution for local environments *********) + +lemma snv_cpss_lpss_conf: ∀h,g,L1,T1. ⦃h, L1⦄ ⊢ T1 ¡[g] → ∀T2. L1 ⊢ T1 ▶* T2 → + ∀L2. L1 ⊢ ▶* L2 → ⦃h, L2⦄ ⊢ T2 ¡[g]. +#h #g #L1 #T1 #H elim H -L1 -T1 +[ #L1 #k #X #H #L2 #_ + >(cpss_inv_sort1 … H) -X // +| #I #L1 #K1 #V1 #i #HLK1 #_ #IHV1 #W2 #H #L2 #HL12 + elim (cpss_inv_lref1 … H) -H + [ #H destruct + elim (lpss_ldrop_conf … HLK1 … HL12) -L1 #X #H #HLK2 + elim (lpss_inv_pair1 … H) -H #K2 #V2 #HK12 #HV12 #H destruct + lapply (IHV1 … HV12 … HK12) -IHV1 -HV12 -HK12 /2 width=5/ + | * #K0 #V0 #V2 #HLK0 #HV12 #HVW2 + lapply (ldrop_mono … HLK0 … HLK1) -HLK0 #H destruct + elim (lpss_ldrop_conf … HLK1 … HL12) -L1 #X #H #HLK2 + elim (lpss_inv_pair1 … H) -H #K2 #V #HK12 #_ #H destruct + lapply (ldrop_fwd_ldrop2 … HLK2) -V #HLK2 + lapply (IHV1 … HV12 … HK12) -IHV1 -HV12 -HK12 /2 width=7/ + ] +| #a #I #L1 #V1 #T1 #_ #_ #IHV1 #IHT1 #X #H #L2 #HL12 + elim (cpss_inv_bind1 … H) -H #V2 #T2 #HV12 #HT12 #H destruct + lapply (IHV1 … HV12 … HL12) -IHV1 #HV2 + lapply (IHT1 … HT12 (L2.ⓑ{I}V2) ?) -IHT1 -HT12 /2 width=1/ +| #a #L1 #V1 #W1 #W0 #T1 #U1 #l #_ #_ #HVW1 #HW10 #HTU1 #IHV1 #IHT1 #X #H #L2 #HL12 + elim (cpss_inv_flat1 … H) -H #V2 #T2 #HV12 #HT12 #H destruct + lapply (IHV1 … HV12 … HL12) -IHV1 #HV2 + lapply (IHT1 … HT12 … HL12) -IHT1 #HT2 + elim (ssta_cpss_lpss_conf … HVW1 … HV12 … HL12) -V1 #W2 #HVW2 #HW12 + elim (dxprs_cpss_lpss_conf … HTU1 … HT12 … HL12) -T1 #X #HTU2 #H + elim (cpss_inv_bind1 … H) -H #W #U2 #HW0 #_ #H -U1 destruct + elim (cprs_cpss2_lpss_conf_dx … HW10 … HW12 … HW0 … HL12) -L1 -W1 -W0 #W0 #HW20 #HW0 + lapply (dxprs_strap1 … (ⓛ{a}W0.U2) HTU2 ?) -HTU2 /3 width=3/ -HW0 /2 width=8/ +| #L1 #W1 #T1 #U1 #l #_ #_ #HTU1 #HUW1 #IHW1 #IHT1 #X #H #L2 #HL12 + elim (cpss_inv_flat1 … H) -H #W2 #T2 #HW12 #HT12 #H destruct + lapply (IHW1 … HW12 … HL12) -IHW1 #HW2 + lapply (IHT1 … HT12 … HL12) -IHT1 #HT2 + elim (ssta_cpss_lpss_conf … HTU1 … HT12 … HL12) -T1 #U2 #HTU2 #HU12 + lapply (cpcs_cpss2_lpss_conf … HUW1 … HU12 … HW12 … HL12) -L1 -W1 -U1 /2 width=4/ +] +qed-. + +lemma snv_lpss_conf: ∀h,g,L1,T. ⦃h, L1⦄ ⊢ T ¡[g] → + ∀L2. L1 ⊢ ▶* L2 → ⦃h, L2⦄ ⊢ T ¡[g]. +#h #g #L1 #T #HT #L2 #HL12 +@(snv_cpss_lpss_conf … HT … HL12) // +qed-. + +lemma snv_cpss_conf: ∀h,g,L,T1. ⦃h, L⦄ ⊢ T1 ¡[g] → + ∀T2. L ⊢ T1 ▶* T2 → ⦃h, L⦄ ⊢ T2 ¡[g]. +#h #g #L #T1 #HT1 #T2 #HT12 +@(snv_cpss_lpss_conf … HT1 … HT12) // +qed-. diff --git a/matita/matita/contribs/lambdadelta/basic_2/dynamic/snv_ltpss_dx.ma b/matita/matita/contribs/lambdadelta/basic_2/dynamic/snv_ltpss_dx.ma deleted file mode 100644 index ca55239f0..000000000 --- a/matita/matita/contribs/lambdadelta/basic_2/dynamic/snv_ltpss_dx.ma +++ /dev/null @@ -1,87 +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/dxprs_ltpss_dx.ma". -include "basic_2/equivalence/cpcs_ltpss_dx.ma". -include "basic_2/dynamic/snv_lift.ma". - -(* STRATIFIED NATIVE VALIDITY FOR TERMS *************************************) - -(* Properties about dx parallel unfold **************************************) - -lemma snv_ltpss_dx_tpss_conf: ∀h,g,L1,T1. ⦃h, L1⦄ ⊢ T1 ¡[g] → - ∀L2,d,e. L1 ▶* [d, e] L2 → - ∀T2. L2 ⊢ T1 ▶* [d, e] T2 → ⦃h, L2⦄ ⊢ T2 ¡[g]. -#h #g #L1 #T1 #H elim H -L1 -T1 -[ #L1 #k #L2 #d #e #_ #X #H - >(tpss_inv_sort1 … H) -X // -| #I #L1 #K1 #V1 #i #HLK1 #HV1 #IHV1 #L2 #d #e #HL12 #X #H - elim (tpss_inv_lref1 … H) -H - [ #H destruct - elim (lt_or_ge i d) #Hdi [ | elim (lt_or_ge i (d + e)) #Hide ] - [ elim (ltpss_dx_ldrop_conf_le … HL12 … HLK1 …) -L1 /2 width=2/ #X #H #HLK2 - elim (ltpss_dx_inv_tpss11 … H …) -H /2 width=1/ #K2 #V2 #HK12 #HV12 #H destruct - lapply (IHV1 … HK12 … HV12) -IHV1 -HK12 -HV12 /2 width=5/ - | elim (ltpss_dx_ldrop_conf_be … HL12 … HLK1 …) -L1 // /2 width=2/ #X #H #HLK2 - elim (ltpss_dx_inv_tpss21 … H …) -H /2 width=1/ #K2 #V2 #HK12 #HV12 #H destruct - lapply (IHV1 … HK12 … HV12) -IHV1 -HK12 -HV12 /2 width=5/ - | lapply (ltpss_dx_ldrop_conf_ge … HL12 … HLK1 ?) -L1 // -Hide /2 width=5/ - ] - | * #K2 #V2 #W2 #Hdi #Hide #HLK2 #HVW2 #HWT2 - elim (ltpss_dx_ldrop_conf_be … HL12 … HLK1 …) -L1 // /2 width=2/ #X #H1 #H2 - elim (ltpss_dx_inv_tpss21 … H1 …) -H1 /2 width=1/ #K0 #V0 #HK12 #HV12 #H destruct - lapply (ldrop_mono … H2 … HLK2) -H2 #H destruct - lapply (ldrop_fwd_ldrop2 … HLK2) -HLK2 #HLK2 - lapply (tpss_trans_eq … HV12 HVW2) -V2 #HV1W2 - lapply (IHV1 … HK12 … HV1W2) -IHV1 -HK12 -HV1W2 /2 width=7/ - ] -| #a #I #L1 #V1 #T1 #_ #_ #IHV1 #IHT1 #L2 #d #e #HL12 #X #H - elim (tpss_inv_bind1 … H) -H #V2 #T2 #HV12 #HT12 #H destruct - lapply (IHV1 … HL12 … HV12) -IHV1 #HV2 - lapply (IHT1 … HT12) -IHT1 -HT12 /2 width=1/ -| #a #L1 #V1 #W1 #W0 #T1 #U1 #l #_ #_ #HVW1 #HW10 #HTU1 #IHV1 #IHT1 #L2 #d #e #HL12 #X #H - elim (tpss_inv_flat1 … H) -H #V2 #T2 #HV12 #HT12 #H destruct - lapply (IHV1 … HL12 … HV12) -IHV1 #HV2 - lapply (IHT1 … HT12) -IHT1 /2 width=1/ #HT2 - elim (ssta_ltpss_dx_tpss_conf … HVW1 … HL12 … HV12) -V1 #W2 #HVW2 #HW12 - elim (dxprs_ltpss_dx_tpss_conf … HTU1 … HL12 … HT12) -T1 #X #HTU2 #H - elim (tpss_inv_bind1 … H) -H #W #U2 #HW0 #_ #H -U1 destruct - elim (cprs_ltpss_dx_tpss2_conf … HW10 … HL12 … HW12 … HW0) -L1 -W1 -W0 #W0 #HW20 #HW0 - lapply (dxprs_strap1 … (ⓛ{a}W0.U2) HTU2 ?) -HTU2 /3 width=3/ -HW0 /2 width=8/ -| #L1 #W1 #T1 #U1 #l #_ #_ #HTU1 #HUW1 #IHW1 #IHT1 #L2 #d #e #HL12 #X #H - elim (tpss_inv_flat1 … H) -H #W2 #T2 #HW12 #HT12 #H destruct - lapply (IHW1 … HL12 … HW12) -IHW1 #HW2 - lapply (IHT1 … HL12 … HT12) -IHT1 #HT2 - elim (ssta_ltpss_dx_tpss_conf … HTU1 … HL12 … HT12) -T1 #U2 #HTU2 #HU12 - lapply (cpcs_ltpss_dx_tpss2_conf … HL12 … HUW1 … HU12 … HW12) -L1 -W1 -U1 /2 width=4/ -] -qed-. - -lemma snv_ltpss_dx_conf: ∀h,g,L1,T. ⦃h, L1⦄ ⊢ T ¡[g] → - ∀L2,d,e. L1 ▶* [d, e] L2 → ⦃h, L2⦄ ⊢ T ¡[g]. -#h #g #L1 #T #HT #L2 #d #e #HL12 -@(snv_ltpss_dx_tpss_conf … HT … HL12) // -qed-. - -lemma snv_tpss_conf: ∀h,g,L,T1. ⦃h, L⦄ ⊢ T1 ¡[g] → - ∀T2,d,e. L ⊢ T1 ▶* [d, e] T2 → ⦃h, L⦄ ⊢ T2 ¡[g]. -#h #g #L #T1 #HT1 #T2 #d #e #HT12 -@(snv_ltpss_dx_tpss_conf … HT1 … HT12) // -qed-. - -lemma snv_tps_conf: ∀h,g,L,T1. ⦃h, L⦄ ⊢ T1 ¡[g] → - ∀T2,d,e. L ⊢ T1 ▶ [d, e] T2 → ⦃h, L⦄ ⊢ T2 ¡[g]. -#h #g #L #T1 #HT1 #T2 #d #e #HT12 -@(snv_tpss_conf … HT1 T2) /2 width=3/ -qed-. diff --git a/matita/matita/contribs/lambdadelta/basic_2/dynamic/snv_ltpss_sn.ma b/matita/matita/contribs/lambdadelta/basic_2/dynamic/snv_ltpss_sn.ma deleted file mode 100644 index 3c8070249..000000000 --- a/matita/matita/contribs/lambdadelta/basic_2/dynamic/snv_ltpss_sn.ma +++ /dev/null @@ -1,28 +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_ltpss_dx.ma". - -(* STRATIFIED NATIVE VALIDITY FOR TERMS *************************************) - -(* Properties about sn parallel unfold **************************************) - -lemma snv_ltpss_sn_conf: ∀h,g,L1,L2,d,e. L1 ⊢ ▶* [d, e] L2 → - ∀T. ⦃h, L1⦄ ⊢ T ¡[g] → ⦃h, L2⦄ ⊢ T ¡[g]. -#h #g #L1 #L2 #d #e #H -lapply (ltpss_sn_ltpssa … H) -H #H @(ltpssa_ind … H) -L2 // -#L #L2 #_ #HL2 #IHL1 #T1 #HT1 -lapply (IHL1 … HT1) -IHL1 -HT1 #HT1 -lapply (snv_ltpss_dx_conf … HT1 … HL2) -HT1 -HL2 // -qed-. diff --git a/matita/matita/contribs/lambdadelta/basic_2/dynamic/snv_sstas.ma b/matita/matita/contribs/lambdadelta/basic_2/dynamic/snv_sstas.ma index 0bdfd7496..a663fecfc 100644 --- a/matita/matita/contribs/lambdadelta/basic_2/dynamic/snv_sstas.ma +++ b/matita/matita/contribs/lambdadelta/basic_2/dynamic/snv_sstas.ma @@ -12,7 +12,7 @@ (* *) (**************************************************************************) -include "basic_2/unwind/sstas_lift.ma". +include "basic_2/unfold/sstas_lift.ma". include "basic_2/dynamic/snv.ma". (* STRATIFIED NATIVE VALIDITY FOR TERMS *************************************) diff --git a/matita/matita/contribs/lambdadelta/basic_2/dynamic/ygt.ma b/matita/matita/contribs/lambdadelta/basic_2/dynamic/ygt.ma index 3b55fca99..c1b30c334 100644 --- a/matita/matita/contribs/lambdadelta/basic_2/dynamic/ygt.ma +++ b/matita/matita/contribs/lambdadelta/basic_2/dynamic/ygt.ma @@ -20,7 +20,7 @@ include "basic_2/dynamic/yprs.ma". inductive ygt (h) (g) (L1) (T1): relation2 lenv term ≝ | ygt_inj : ∀L,L2,T,T2. h ⊢ ⦃L1, T1⦄ ≥[g] ⦃L, T⦄ → h ⊢ ⦃L, T⦄ ≻[g] ⦃L2, T2⦄ → ygt h g L1 T1 L2 T2 -| ygt_step: ∀L,L2,T. ygt h g L1 T1 L T → L ➡ L2 → ygt h g L1 T1 L2 T +| ygt_step: ∀L,L2,T. ygt h g L1 T1 L T → L ⊢ ➡ L2 → ygt h g L1 T1 L2 T . interpretation "'big tree' proper parallel computation (closure)" @@ -31,7 +31,7 @@ interpretation "'big tree' proper parallel computation (closure)" lemma ygt_fwd_yprs: ∀h,g,L1,L2,T1,T2. h ⊢ ⦃L1, T1⦄ >[g] ⦃L2, T2⦄ → h ⊢ ⦃L1, T1⦄ ≥[g] ⦃L2, T2⦄. #h #g #L1 #L2 #T1 #T2 #H elim H -L2 -T2 -/3 width=4 by yprs_strap1, ysc_ypr, ypr_ltpr/ +/3 width=4 by yprs_strap1, ysc_ypr, ypr_lpr/ qed-. (* Basic properties *********************************************************) diff --git a/matita/matita/contribs/lambdadelta/basic_2/dynamic/ypr.ma b/matita/matita/contribs/lambdadelta/basic_2/dynamic/ypr.ma index 9135495f8..b1c75077e 100644 --- a/matita/matita/contribs/lambdadelta/basic_2/dynamic/ypr.ma +++ b/matita/matita/contribs/lambdadelta/basic_2/dynamic/ypr.ma @@ -12,14 +12,14 @@ (* *) (**************************************************************************) -include "basic_2/reducibility/ltpr.ma". +include "basic_2/reduction/lpr.ma". include "basic_2/dynamic/lsubsv.ma". (* "BIG TREE" PARALLEL REDUCTION FOR CLOSURES *******************************) inductive ypr (h) (g) (L1) (T1): relation2 lenv term ≝ | ypr_fw : ∀L2,T2. ♯{L2, T2} < ♯{L1, T1} → ypr h g L1 T1 L2 T2 -| ypr_ltpr : ∀L2. L1 ➡ L2 → ypr h g L1 T1 L2 T1 +| ypr_lpr : ∀L2. L1 ⊢ ➡ L2 → ypr h g L1 T1 L2 T1 | ypr_cpr : ∀T2. L1 ⊢ T1 ➡ T2 → ypr h g L1 T1 L1 T2 | ypr_ssta : ∀T2,l. ⦃h, L1⦄ ⊢ T1 •[g] ⦃l+1, T2⦄ → ypr h g L1 T1 L1 T2 | ypr_lsubsv: ∀L2. h ⊢ L2 ¡⊑[g] L1 → ypr h g L1 T1 L2 T1 diff --git a/matita/matita/contribs/lambdadelta/basic_2/dynamic/yprs.ma b/matita/matita/contribs/lambdadelta/basic_2/dynamic/yprs.ma index 0c7231075..bb4daf0be 100644 --- a/matita/matita/contribs/lambdadelta/basic_2/dynamic/yprs.ma +++ b/matita/matita/contribs/lambdadelta/basic_2/dynamic/yprs.ma @@ -12,7 +12,7 @@ (* *) (**************************************************************************) -include "basic_2/computation/ltprs.ma". +include "basic_2/computation/lprs.ma". include "basic_2/dynamic/ypr.ma". (* "BIG TREE" PARALLEL COMPUTATION FOR CLOSURES *****************************) @@ -60,8 +60,8 @@ lemma cprs_yprs: ∀h,g,L,T1,T2. L ⊢ T1 ➡* T2 → h ⊢ ⦃L, T1⦄ ≥[g] #h #g #L #T1 #T2 #H @(cprs_ind … H) -T2 // /3 width=4 by ypr_cpr, yprs_strap1/ qed. -lemma ltprs_yprs: ∀h,g,L1,L2,T. L1 ➡* L2 → h ⊢ ⦃L1, T⦄ ≥[g] ⦃L2, T⦄. -#h #g #L1 #L2 #T #H @(ltprs_ind … H) -L2 // /3 width=4 by ypr_ltpr, yprs_strap1/ +lemma lprs_yprs: ∀h,g,L1,L2,T. L1 ⊢ ➡* L2 → h ⊢ ⦃L1, T⦄ ≥[g] ⦃L2, T⦄. +#h #g #L1 #L2 #T #H @(lprs_ind … H) -L2 // /3 width=4 by ypr_lpr, yprs_strap1/ qed. lemma sstas_yprs: ∀h,g,L,T1,T2. ⦃h, L⦄ ⊢ T1 •*[g] T2 → @@ -72,7 +72,7 @@ qed. lemma lsubsv_yprs: ∀h,g,L1,L2,T. h ⊢ L2 ¡⊑[g] L1 → h ⊢ ⦃L1, T⦄ ≥[g] ⦃L2, T⦄. /3 width=1/ qed. -lemma ltpr_cprs_yprs: ∀h,g,L1,L2,T1,T2. L1 ➡ L2 → L2 ⊢ T1 ➡* T2 → - h ⊢ ⦃L1, T1⦄ ≥[g] ⦃L2, T2⦄. -/3 width=4 by yprs_strap2, ypr_ltpr, cprs_yprs/ +lemma lpr_cprs_yprs: ∀h,g,L1,L2,T1,T2. L1 ⊢ ➡ L2 → L2 ⊢ T1 ➡* T2 → + h ⊢ ⦃L1, T1⦄ ≥[g] ⦃L2, T2⦄. +/3 width=4 by yprs_strap2, ypr_lpr, cprs_yprs/ qed. diff --git a/matita/matita/contribs/lambdadelta/basic_2/dynamic/ysc.ma b/matita/matita/contribs/lambdadelta/basic_2/dynamic/ysc.ma index 203cf3ebd..88d19aea1 100644 --- a/matita/matita/contribs/lambdadelta/basic_2/dynamic/ysc.ma +++ b/matita/matita/contribs/lambdadelta/basic_2/dynamic/ysc.ma @@ -37,7 +37,7 @@ qed. (* Inversion lemmas on "big tree" parallel reduction for closures ***********) lemma ypr_inv_ysc: ∀h,g,L1,L2,T1,T2. h ⊢ ⦃L1, T1⦄ ≽[g] ⦃L2, T2⦄ → - h ⊢ ⦃L1, T1⦄ ≻[g] ⦃L2, T2⦄ ∨ (L1 ➡ L2 ∧ T1 = T2). + h ⊢ ⦃L1, T1⦄ ≻[g] ⦃L2, T2⦄ ∨ (L1 ⊢ ➡ L2 ∧ T1 = T2). #h #g #L1 #L2 #T1 #T2 * -L2 -T2 /3 width=1/ /3 width=2/ [ #T2 #HT12 elim (term_eq_dec T1 T2) #H destruct /3 width=1/ /4 width=1/ | #L2 #HL21 elim (lenv_eq_dec L1 L2) #H destruct /3 width=1/ /4 width=1/ diff --git a/matita/matita/contribs/lambdadelta/basic_2/equivalence/cpcs.ma b/matita/matita/contribs/lambdadelta/basic_2/equivalence/cpcs.ma index 49f490bce..e4388e3b2 100644 --- a/matita/matita/contribs/lambdadelta/basic_2/equivalence/cpcs.ma +++ b/matita/matita/contribs/lambdadelta/basic_2/equivalence/cpcs.ma @@ -85,11 +85,21 @@ lemma cpcs_cpss_strap1: ∀L,T1,T. L ⊢ T1 ⬌* T → ∀T2. L ⊢ T ▶* T2 @(cpcs_cpr_strap1 … HT1) -T1 /2 width=3/ qed-. +lemma cpcs_cpss_strap2: ∀L,T1,T. L ⊢ T1 ▶* T → ∀T2. L ⊢ T ⬌* T2 → L ⊢ T1 ⬌* T2. +#L #T1 #T #HT1 #T2 #HT2 +@(cpcs_cpr_strap2 … HT2) -T2 /2 width=3/ +qed-. + lemma cpcs_cpss_conf: ∀L,T,T1. L ⊢ T ▶* T1 → ∀T2. L ⊢ T ⬌* T2 → L ⊢ T1 ⬌* T2. #L #T #T1 #HT1 #T2 #HT2 @(cpcs_cpr_conf … HT2) -T2 /2 width=3/ qed-. +lemma cpcs_cpss_div: ∀L,T1,T. L ⊢ T1 ⬌* T → ∀T2. L ⊢ T2 ▶* T → L ⊢ T1 ⬌* T2. +#L #T1 #T #HT1 #T2 #HT2 +@(cpcs_cpr_div … HT1) -T1 /2 width=3/ +qed-. + (* Basic_1: removed theorems 9: clear_pc3_trans pc3_ind_left pc3_head_1 pc3_head_2 pc3_head_12 pc3_head_21 diff --git a/matita/matita/contribs/lambdadelta/basic_2/equivalence/cpcs_lpss.ma b/matita/matita/contribs/lambdadelta/basic_2/equivalence/cpcs_lpss.ma index c9bcdc83d..3da649bc5 100644 --- a/matita/matita/contribs/lambdadelta/basic_2/equivalence/cpcs_lpss.ma +++ b/matita/matita/contribs/lambdadelta/basic_2/equivalence/cpcs_lpss.ma @@ -20,8 +20,9 @@ include "basic_2/equivalence/cpcs_cpcs.ma". (* Properties on sn parallel substitution for local environments ************) -lemma cpcs_lpss_conf: ∀L1,L2. L1 ⊢ ▶* L2 → ∀T1,T2. L1 ⊢ T1 ⬌* T2 → L2 ⊢ T1 ⬌* T2. -#L1 #L2 #HL12 #T1 #T2 #H +lemma cpcs_lpss_conf: ∀L1,T1,T2. L1 ⊢ T1 ⬌* T2 → + ∀L2. L1 ⊢ ▶* L2 → L2 ⊢ T1 ⬌* T2. +#L1 #T1 #T2 #H #L2 #HL12 elim (cpcs_inv_cprs … H) -H #T #HT1 #HT2 elim (cprs_lpss_conf_dx … HT1 … HL12) -HT1 #U1 #H1 #HTU1 elim (cprs_lpss_conf_dx … HT2 … HL12) -L1 #U2 #H2 #HTU2 @@ -30,19 +31,21 @@ lapply (cprs_cpss_trans … HTU1 … HU1) -U1 lapply (cprs_cpss_trans … HTU2 … HU2) -U2 /2 width=3/ qed-. -lemma cpcs_lpss_cpss_conf: ∀L1,L2. L1 ⊢ ▶* L2 → - ∀T,T2. L1 ⊢ T ⬌* T2 → - ∀T1. L2 ⊢ T ▶* T1 → - L2 ⊢ T1 ⬌* T2. -#L1 #L2 #HL12 #T #T2 #HT2 #T1 #HT1 -lapply (cpcs_lpss_conf … HL12 … HT2) -L1 #HT2 -lapply (cpcs_cpss_conf … HT1 … HT2) -T // +lemma cpcs_cpss_lpss_conf: ∀L1,T,T2. L1 ⊢ T ⬌* T2 → ∀T1. L1 ⊢ T ▶* T1 → + ∀L2. L1 ⊢ ▶* L2 → L2 ⊢ T1 ⬌* T2. +#L1 #T #T2 #HT2 #T1 #HT1 #L2 #HL12 +lapply (cpcs_lpss_conf … HT2 … HL12) -HT2 #HT2 +elim (lpss_cpss_conf_dx … HT1 … HL12) -L1 #T0 #HT0 #HT10 +lapply (cpcs_cpss_conf … HT0 … HT2) -T #HT02 +lapply (cpcs_cpss_strap2 … HT10 … HT02) -T0 // qed-. -lemma cpcs_lpss_cpss2_conf: ∀L1,L2. L1 ⊢ ▶* L2 → ∀T1,T2. L1 ⊢ T1 ⬌* T2 → - ∀T3. L2 ⊢ T1 ▶* T3 → ∀T4. L2 ⊢ T2 ▶* T4 → - L2 ⊢ T3 ⬌* T4. -#L1 #L2 #HL12 #T1 #T2 #HT12 #T3 #HT13 #T4 #HT24 -lapply (cpcs_lpss_cpss_conf … HL12 … HT12 … HT13) -L1 -T1 #HT32 -lapply (cpcs_cpss_strap1 … HT32 … HT24) -T2 // +lemma cpcs_cpss2_lpss_conf: ∀L1,T1,T2. L1 ⊢ T1 ⬌* T2 → + ∀T3. L1 ⊢ T1 ▶* T3 → ∀T4. L1 ⊢ T2 ▶* T4 → + ∀L2. L1 ⊢ ▶* L2 → L2 ⊢ T3 ⬌* T4. +#L1 #T1 #T2 #HT12 #T3 #HT13 #T4 #HT24 #L2 #HL12 +lapply (cpcs_cpss_lpss_conf … HT12 … HT13 … HL12) -T1 #HT32 +elim (lpss_cpss_conf_dx … HT24 … HL12) -L1 #T #HT2 #HT4 +lapply (cpcs_cpss_strap1 … HT32 … HT2) -T2 #HT3 +lapply (cpcs_cpss_div … HT3 … HT4) -T // qed-. diff --git a/matita/matita/contribs/lambdadelta/basic_2/etc/cpr/snv_ltpss_dx.etc b/matita/matita/contribs/lambdadelta/basic_2/etc/cpr/snv_ltpss_dx.etc new file mode 100644 index 000000000..ca55239f0 --- /dev/null +++ b/matita/matita/contribs/lambdadelta/basic_2/etc/cpr/snv_ltpss_dx.etc @@ -0,0 +1,87 @@ +(**************************************************************************) +(* ___ *) +(* ||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/dxprs_ltpss_dx.ma". +include "basic_2/equivalence/cpcs_ltpss_dx.ma". +include "basic_2/dynamic/snv_lift.ma". + +(* STRATIFIED NATIVE VALIDITY FOR TERMS *************************************) + +(* Properties about dx parallel unfold **************************************) + +lemma snv_ltpss_dx_tpss_conf: ∀h,g,L1,T1. ⦃h, L1⦄ ⊢ T1 ¡[g] → + ∀L2,d,e. L1 ▶* [d, e] L2 → + ∀T2. L2 ⊢ T1 ▶* [d, e] T2 → ⦃h, L2⦄ ⊢ T2 ¡[g]. +#h #g #L1 #T1 #H elim H -L1 -T1 +[ #L1 #k #L2 #d #e #_ #X #H + >(tpss_inv_sort1 … H) -X // +| #I #L1 #K1 #V1 #i #HLK1 #HV1 #IHV1 #L2 #d #e #HL12 #X #H + elim (tpss_inv_lref1 … H) -H + [ #H destruct + elim (lt_or_ge i d) #Hdi [ | elim (lt_or_ge i (d + e)) #Hide ] + [ elim (ltpss_dx_ldrop_conf_le … HL12 … HLK1 …) -L1 /2 width=2/ #X #H #HLK2 + elim (ltpss_dx_inv_tpss11 … H …) -H /2 width=1/ #K2 #V2 #HK12 #HV12 #H destruct + lapply (IHV1 … HK12 … HV12) -IHV1 -HK12 -HV12 /2 width=5/ + | elim (ltpss_dx_ldrop_conf_be … HL12 … HLK1 …) -L1 // /2 width=2/ #X #H #HLK2 + elim (ltpss_dx_inv_tpss21 … H …) -H /2 width=1/ #K2 #V2 #HK12 #HV12 #H destruct + lapply (IHV1 … HK12 … HV12) -IHV1 -HK12 -HV12 /2 width=5/ + | lapply (ltpss_dx_ldrop_conf_ge … HL12 … HLK1 ?) -L1 // -Hide /2 width=5/ + ] + | * #K2 #V2 #W2 #Hdi #Hide #HLK2 #HVW2 #HWT2 + elim (ltpss_dx_ldrop_conf_be … HL12 … HLK1 …) -L1 // /2 width=2/ #X #H1 #H2 + elim (ltpss_dx_inv_tpss21 … H1 …) -H1 /2 width=1/ #K0 #V0 #HK12 #HV12 #H destruct + lapply (ldrop_mono … H2 … HLK2) -H2 #H destruct + lapply (ldrop_fwd_ldrop2 … HLK2) -HLK2 #HLK2 + lapply (tpss_trans_eq … HV12 HVW2) -V2 #HV1W2 + lapply (IHV1 … HK12 … HV1W2) -IHV1 -HK12 -HV1W2 /2 width=7/ + ] +| #a #I #L1 #V1 #T1 #_ #_ #IHV1 #IHT1 #L2 #d #e #HL12 #X #H + elim (tpss_inv_bind1 … H) -H #V2 #T2 #HV12 #HT12 #H destruct + lapply (IHV1 … HL12 … HV12) -IHV1 #HV2 + lapply (IHT1 … HT12) -IHT1 -HT12 /2 width=1/ +| #a #L1 #V1 #W1 #W0 #T1 #U1 #l #_ #_ #HVW1 #HW10 #HTU1 #IHV1 #IHT1 #L2 #d #e #HL12 #X #H + elim (tpss_inv_flat1 … H) -H #V2 #T2 #HV12 #HT12 #H destruct + lapply (IHV1 … HL12 … HV12) -IHV1 #HV2 + lapply (IHT1 … HT12) -IHT1 /2 width=1/ #HT2 + elim (ssta_ltpss_dx_tpss_conf … HVW1 … HL12 … HV12) -V1 #W2 #HVW2 #HW12 + elim (dxprs_ltpss_dx_tpss_conf … HTU1 … HL12 … HT12) -T1 #X #HTU2 #H + elim (tpss_inv_bind1 … H) -H #W #U2 #HW0 #_ #H -U1 destruct + elim (cprs_ltpss_dx_tpss2_conf … HW10 … HL12 … HW12 … HW0) -L1 -W1 -W0 #W0 #HW20 #HW0 + lapply (dxprs_strap1 … (ⓛ{a}W0.U2) HTU2 ?) -HTU2 /3 width=3/ -HW0 /2 width=8/ +| #L1 #W1 #T1 #U1 #l #_ #_ #HTU1 #HUW1 #IHW1 #IHT1 #L2 #d #e #HL12 #X #H + elim (tpss_inv_flat1 … H) -H #W2 #T2 #HW12 #HT12 #H destruct + lapply (IHW1 … HL12 … HW12) -IHW1 #HW2 + lapply (IHT1 … HL12 … HT12) -IHT1 #HT2 + elim (ssta_ltpss_dx_tpss_conf … HTU1 … HL12 … HT12) -T1 #U2 #HTU2 #HU12 + lapply (cpcs_ltpss_dx_tpss2_conf … HL12 … HUW1 … HU12 … HW12) -L1 -W1 -U1 /2 width=4/ +] +qed-. + +lemma snv_ltpss_dx_conf: ∀h,g,L1,T. ⦃h, L1⦄ ⊢ T ¡[g] → + ∀L2,d,e. L1 ▶* [d, e] L2 → ⦃h, L2⦄ ⊢ T ¡[g]. +#h #g #L1 #T #HT #L2 #d #e #HL12 +@(snv_ltpss_dx_tpss_conf … HT … HL12) // +qed-. + +lemma snv_tpss_conf: ∀h,g,L,T1. ⦃h, L⦄ ⊢ T1 ¡[g] → + ∀T2,d,e. L ⊢ T1 ▶* [d, e] T2 → ⦃h, L⦄ ⊢ T2 ¡[g]. +#h #g #L #T1 #HT1 #T2 #d #e #HT12 +@(snv_ltpss_dx_tpss_conf … HT1 … HT12) // +qed-. + +lemma snv_tps_conf: ∀h,g,L,T1. ⦃h, L⦄ ⊢ T1 ¡[g] → + ∀T2,d,e. L ⊢ T1 ▶ [d, e] T2 → ⦃h, L⦄ ⊢ T2 ¡[g]. +#h #g #L #T1 #HT1 #T2 #d #e #HT12 +@(snv_tpss_conf … HT1 T2) /2 width=3/ +qed-. diff --git a/matita/matita/contribs/lambdadelta/basic_2/etc/cpr/snv_ltpss_sn.etc b/matita/matita/contribs/lambdadelta/basic_2/etc/cpr/snv_ltpss_sn.etc new file mode 100644 index 000000000..3c8070249 --- /dev/null +++ b/matita/matita/contribs/lambdadelta/basic_2/etc/cpr/snv_ltpss_sn.etc @@ -0,0 +1,28 @@ +(**************************************************************************) +(* ___ *) +(* ||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_ltpss_dx.ma". + +(* STRATIFIED NATIVE VALIDITY FOR TERMS *************************************) + +(* Properties about sn parallel unfold **************************************) + +lemma snv_ltpss_sn_conf: ∀h,g,L1,L2,d,e. L1 ⊢ ▶* [d, e] L2 → + ∀T. ⦃h, L1⦄ ⊢ T ¡[g] → ⦃h, L2⦄ ⊢ T ¡[g]. +#h #g #L1 #L2 #d #e #H +lapply (ltpss_sn_ltpssa … H) -H #H @(ltpssa_ind … H) -L2 // +#L #L2 #_ #HL2 #IHL1 #T1 #HT1 +lapply (IHL1 … HT1) -IHL1 -HT1 #HT1 +lapply (snv_ltpss_dx_conf … HT1 … HL2) -HT1 -HL2 // +qed-. diff --git a/matita/matita/contribs/lambdadelta/basic_2/static/ssta_lpss.ma b/matita/matita/contribs/lambdadelta/basic_2/static/ssta_lpss.ma index 5012fd975..7471b2304 100644 --- a/matita/matita/contribs/lambdadelta/basic_2/static/ssta_lpss.ma +++ b/matita/matita/contribs/lambdadelta/basic_2/static/ssta_lpss.ma @@ -20,7 +20,7 @@ include "basic_2/static/ssta_lift.ma". (* Properties about sn parallel substitution ********************************) (* Note: apparently this was missing in basic_1 *) -lemma ssta_tpss_lpss_conf: ∀h,g,L1,T1,U1,l. ⦃h, L1⦄ ⊢ T1 •[g] ⦃l, U1⦄ → +lemma ssta_cpss_lpss_conf: ∀h,g,L1,T1,U1,l. ⦃h, L1⦄ ⊢ T1 •[g] ⦃l, U1⦄ → ∀T2. L1 ⊢ T1 ▶* T2 → ∀L2. L1 ⊢ ▶* L2 → ∃∃U2. ⦃h, L2⦄ ⊢ T2 •[g] ⦃l, U2⦄ & L1 ⊢ U1 ▶* U2. #h #g #L1 #T1 #U1 #l #H elim H -L1 -T1 -U1 -l @@ -73,9 +73,9 @@ qed-. lemma ssta_cpss_conf: ∀h,g,L,T1,U1,l. ⦃h, L⦄ ⊢ T1 •[g] ⦃l, U1⦄ → ∀T2. L ⊢ T1 ▶* T2 → ∃∃U2. ⦃h, L⦄ ⊢ T2 •[g] ⦃l, U2⦄ & L ⊢ U1 ▶* U2. -/2 width=3 by ssta_tpss_lpss_conf/ qed-. +/2 width=3 by ssta_cpss_lpss_conf/ qed-. lemma ssta_lpss_conf: ∀h,g,L1,T,U1,l. ⦃h, L1⦄ ⊢ T •[g] ⦃l, U1⦄ → ∀L2. L1 ⊢ ▶* L2 → ∃∃U2. ⦃h, L2⦄ ⊢ T •[g] ⦃l, U2⦄ & L1 ⊢ U1 ▶* U2. -/2 width=3 by ssta_tpss_lpss_conf/ qed-. +/2 width=3 by ssta_cpss_lpss_conf/ qed-. diff --git a/matita/matita/contribs/lambdadelta/basic_2/unfold/sstas_lpss.ma b/matita/matita/contribs/lambdadelta/basic_2/unfold/sstas_lpss.ma index 8f9eda109..3ecbc2256 100644 --- a/matita/matita/contribs/lambdadelta/basic_2/unfold/sstas_lpss.ma +++ b/matita/matita/contribs/lambdadelta/basic_2/unfold/sstas_lpss.ma @@ -17,23 +17,23 @@ include "basic_2/unfold/sstas.ma". (* ITERATED STRATIFIED STATIC TYPE ASSIGNMENT FOR TERMS *********************) -(* Properties about sn parallel substitution ********************************) +(* Properties about sn parallel substitution for local environments *********) -lemma sstas_tpss_lpss_conf: ∀h,g,L1,T1,U1. ⦃h, L1⦄ ⊢ T1 •*[g] U1 → +lemma sstas_cpss_lpss_conf: ∀h,g,L1,T1,U1. ⦃h, L1⦄ ⊢ T1 •*[g] U1 → ∀T2. L1 ⊢ T1 ▶* T2 → ∀L2. L1 ⊢ ▶* L2 → ∃∃U2. ⦃h, L2⦄ ⊢ T2 •*[g] U2 & L1 ⊢ U1 ▶* U2. #h #g #L1 #T1 #U1 #H @(sstas_ind_dx … H) -T1 /2 width=3/ #T0 #U0 #l0 #HTU0 #_ #IHU01 #T #HT0 #L2 #HL12 -elim (ssta_tpss_lpss_conf … HTU0 … HT0 … HL12) -HTU0 -HT0 #U #HTU #HU0 +elim (ssta_cpss_lpss_conf … HTU0 … HT0 … HL12) -HTU0 -HT0 #U #HTU #HU0 elim (IHU01 … HU0 … HL12) -IHU01 -U0 -HL12 /3 width=4/ qed-. -lemma sstas_tpss_conf: ∀h,g,L,T1,U1. ⦃h, L⦄ ⊢ T1 •*[g] U1 → +lemma sstas_cpss_conf: ∀h,g,L,T1,U1. ⦃h, L⦄ ⊢ T1 •*[g] U1 → ∀T2. L ⊢ T1 ▶* T2 → ∃∃U2. ⦃h, L⦄ ⊢ T2 •*[g] U2 & L ⊢ U1 ▶* U2. -/2 width=3 by sstas_tpss_lpss_conf/ qed-. +/2 width=3 by sstas_cpss_lpss_conf/ qed-. lemma sstas_lpss_conf: ∀h,g,L1,T,U1. ⦃h, L1⦄ ⊢ T •*[g] U1 → ∀L2. L1 ⊢ ▶* L2 → ∃∃U2. ⦃h, L2⦄ ⊢ T •*[g] U2 & L1 ⊢ U1 ▶* U2. -/2 width=3 by sstas_tpss_lpss_conf/ qed-. +/2 width=3 by sstas_cpss_lpss_conf/ qed-. 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 9a4a98b86..753cddf6f 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 @@ -44,7 +44,7 @@ table { } ] [ { "stratified native validity" * } { - [ "snv ( ⦃?,?⦄ ⊢ ? ¡[?] )" "snv_lift" + "snv_ltpss_dx" + "snv_ltpss_sn" + "snv_aaa" + "snv_ssta" + "snv_sstas" + "snv_ssta_ltpr" + "snv_ltpr" + "snv_cpcs" * ] + [ "snv ( ⦃?,?⦄ ⊢ ? ¡[?] )" "snv_lift" + "snv_lpss" + "snv_aaa" + "snv_ssta" + "snv_sstas" + "snv_ssta_ltpr" + "snv_ltpr" + "snv_cpcs" * ] } ] }