From 0dec595530e6da8ca16af84e40b59c998e6ed4af Mon Sep 17 00:00:00 2001 From: Ferruccio Guidi Date: Fri, 8 Mar 2013 19:48:14 +0000 Subject: [PATCH] second recursive part of preservation finally proved! --- .../lambdadelta/basic_2/dynamic/snv_cpcs.ma | 25 +++++---- .../lambdadelta/basic_2/dynamic/snv_ssta.ma | 51 ++++++++++++------- .../lambdadelta/basic_2/unwind/sstas_sstas.ma | 7 ++- 3 files changed, 52 insertions(+), 31 deletions(-) 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 7f325d41a..1d5f93c49 100644 --- a/matita/matita/contribs/lambdadelta/basic_2/dynamic/snv_cpcs.ma +++ b/matita/matita/contribs/lambdadelta/basic_2/dynamic/snv_cpcs.ma @@ -12,7 +12,7 @@ (* *) (**************************************************************************) -include "basic_2/static/ssta_ssta.ma". +include "basic_2/unwind/sstas_sstas.ma". include "basic_2/computation/ygt.ma". include "basic_2/equivalence/cpcs_ltpr.ma". include "basic_2/dynamic/snv_ltpss_dx.ma". @@ -140,13 +140,16 @@ lapply (ltpr_cprs_conf … HL12 … HWU1) -L1 #HWU1 lapply (cpcs_canc_sn … HW12 HWU1) -W1 #H elim (cpcs_inv_cprs … H) -H /3 width=3/ qed-. -(* -fact sstas_dxprs_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] → - ∀U1. ⦃h, L1⦄ ⊢ T1 •*[g] U1 → ∀T2. ⦃h, L1⦄ ⊢ T1 •*➡*[g] T2 → - ∃∃U2. ⦃h, L1⦄ ⊢ T2 •*[g] U2 & L1 ⊢ U1 ⬌* U2. -#h #g #L0 #T0 #IH3 #IH2 #IH1 #L1 #T1 #H01 #HT1 #U1 #HTU1 #T2 * #T #HT1T #HTT2 -*) + +fact ssta_dxprs_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] → + ∀l,U1. ⦃h, L1⦄ ⊢ T1 •[g, l+1] U1 → ∀T2. ⦃h, L1⦄ ⊢ T1 •*➡*[g] T2 → + ∃∃U,U2. ⦃h, L1⦄ ⊢ U1 •*[g] U & ⦃h, L1⦄ ⊢ T2 •*[g] U2 & L1 ⊢ U ⬌* U2. +#h #g #L0 #T0 #IH2 #IH1 #L1 #T1 #H01 #HT1 #l #U1 #HTU1 #T2 * #T #HT1T #HTT2 +elim (sstas_strip … HT1T … HTU1) #HU1T destruct [ -HT1T | -L0 -T0 -T1 ] +[ elim (ssta_ltpr_cprs_aux … IH2 IH1 … HTU1 L1 … HTT2) // -L0 -T0 -T /3 width=5/ +| @(ex3_2_intro …T2 HU1T) // /2 width=1/ +] +qed-. diff --git a/matita/matita/contribs/lambdadelta/basic_2/dynamic/snv_ssta.ma b/matita/matita/contribs/lambdadelta/basic_2/dynamic/snv_ssta.ma index 2bee82488..f32e1ba01 100644 --- a/matita/matita/contribs/lambdadelta/basic_2/dynamic/snv_ssta.ma +++ b/matita/matita/contribs/lambdadelta/basic_2/dynamic/snv_ssta.ma @@ -18,21 +18,36 @@ include "basic_2/dynamic/snv_cpcs.ma". (* Properties on stratified static type assignment for terms ****************) -fact snv_ssta_aux: ∀h,g,L,T. ( - ∀L0,T0. ⦃h, L0⦄ ⊩ T0 :[g] → - ∀U0,l. ⦃h, L0⦄ ⊢ T0 •[g, l + 1] U0 → - ♯{L0, T0} < ♯{L, T} → ⦃h, L0⦄ ⊩ U0 :[g] - ) → - ∀L0,T0. ⦃h, L0⦄ ⊩ T0 :[g] → - ∀U0,l. ⦃h, L0⦄ ⊢ T0 •[g, l + 1] U0 → - L0 = L → T0 = T → ⦃h, L0⦄ ⊩ U0 :[g]. -#h #g #L #T #IH1 #L0 #T0 * -L0 -T0 -[ -| -| -| #a #L0 #V #W #W0 #T0 #V0 #l0 #HV #HT0 #HVW #HW0 #HTV0 #X #l #H #H1 #H2 destruct - elim (ssta_inv_appl1 … H) -H #U0 #HTU0 #H destruct - lapply (IH1 … HT0 … HTU0 ?) // #HU0 - @(snv_appl … HV HU0 HVW HW0) -HV -HU0 -HVW -HW0 -| #L0 #W #T0 #W0 #l0 #_ #HT0 #_ #_ #U0 #l #H #H1 #H2 destruct -W0 - lapply (ssta_inv_cast1 … H) -H /2 width=5/ +fact snv_ssta_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⦄ → IH_snv_ssta h g L1 T1) → + ∀L1,T1. L0 = L1 → T0 = T1 → IH_snv_ssta h g L1 T1. +#h #g #L0 #T0 #IH3 #IH2 #IH1 #L1 * * [||||*] +[ #k #HL0 #HT0 #_ #X #l #H2 destruct -IH3 -IH2 -IH1 + elim (ssta_inv_sort1 … H2) -H2 #_ #H destruct // +| #i #HL0 #HT0 #H1 #X #l #H2 destruct -IH3 -IH2 + elim (snv_inv_lref … H1) -H1 #I #K1 #V1 #HLK1 #HV1 + elim (ssta_inv_lref1 … H2) -H2 * #K0 #V0 #W1 [| #l ] #H #HVW1 #HX [| #_ ] + lapply (ldrop_mono … H … HLK1) -H #H destruct + lapply (ldrop_pair2_fwd_fw … HLK1 (#i)) #H + lapply (ldrop_fwd_ldrop2 … HLK1) -HLK1 /4 width=7/ +| #p #HL0 #HT0 #H1 #X #l #H2 destruct -IH3 -IH2 -IH1 + elim (snv_inv_gref … H1) +| #a #I #V1 #T1 #HL0 #HT0 #H1 #X #l #H2 destruct -IH3 -IH2 + elim (snv_inv_bind … H1) -H1 #HV1 #HT1 + elim (ssta_inv_bind1 … H2) -H2 #U1 #HTU1 #H destruct /4 width=5/ +| #V1 #T1 #HL0 #HT0 #H1 #X #l #H2 destruct + elim (snv_inv_appl … H1) -H1 #a #W1 #W0 #T0 #l0 #HV1 #HT1 #HVW1 #HW10 #HT10 + elim (ssta_inv_appl1 … H2) -H2 #U1 #HTU1 #H destruct + lapply (IH1 … HT1 … HTU1) -IH1 /2 width=1/ #HU1 + elim (ssta_dxprs_aux … IH3 IH2 … HTU1 … HT10) -IH3 -IH2 // /2 width=2/ -T1 #U #X #HU1U #H #HU0 + elim (sstas_inv_bind1 … H) -H #U0 #HTU0 #H destruct + elim (cpcs_inv_abst2 … HU0) -HU0 #W2 #U2 #HU2 #HU02 + elim (cprs_inv_abst … HU02 Abst W0) -HU02 #HW02 #_ + lapply (cprs_trans … HW10 … HW02) -W0 /3 width=10 by snv_appl, ex2_intro/ (**) (* auto is too slow without trace *) +| #W1 #T1 #HL0 #HT0 #H1 #X #l #H2 destruct -IH3 -IH2 + elim (snv_inv_cast … H1) -H1 #U1 #l0 #HW1 #HT1 #HTU1 #HUW1 + lapply (ssta_inv_cast1 … H2) -H2 /3 width=5/ +] +qed-. diff --git a/matita/matita/contribs/lambdadelta/basic_2/unwind/sstas_sstas.ma b/matita/matita/contribs/lambdadelta/basic_2/unwind/sstas_sstas.ma index f11a078bf..84b941232 100644 --- a/matita/matita/contribs/lambdadelta/basic_2/unwind/sstas_sstas.ma +++ b/matita/matita/contribs/lambdadelta/basic_2/unwind/sstas_sstas.ma @@ -30,7 +30,7 @@ qed-. lemma sstas_strip: ∀h,g,L,T,U1. ⦃h, L⦄ ⊢ T •*[g] U1 → ∀U2,l. ⦃h, L⦄ ⊢ T •[g, l] U2 → - ⦃h, L⦄ ⊢ U1 •[g, l] U2 ∨ ⦃h, L⦄ ⊢ U2 •*[g] U1. + T = U1 ∨ ⦃h, L⦄ ⊢ U2 •*[g] U1. #h #g #L #T #U1 #H1 @(sstas_ind_dx … H1) -T /2 width=1/ #T #U #l0 #HTU #HU1 #_ #U2 #l #H2 elim (ssta_mono … H2 … HTU) -H2 -HTU #H1 #H2 destruct /2 width=1/ @@ -47,5 +47,8 @@ theorem sstas_conf: ∀h,g,L,T,U1. ⦃h, L⦄ ⊢ T •*[g] U1 → ⦃h, L⦄ ⊢ U1 •*[g] U2 ∨ ⦃h, L⦄ ⊢ U2 •*[g] U1. #h #g #L #T #U1 #H1 @(sstas_ind_dx … H1) -T /2 width=1/ #T #U #l #HTU #HU1 #IHU1 #U2 #H2 -elim (sstas_strip … H2 … HTU) -T /2 width=1/ -IHU1 /3 width=4/ +elim (sstas_strip … H2 … HTU) #H destruct +[ -H2 -IHU1 /3 width=4/ +| -T /2 width=1/ +] qed-. -- 2.39.2