From 4b4d24e46ac80c9b035b6c23944d851f9f0ec179 Mon Sep 17 00:00:00 2001 From: Ferruccio Guidi Date: Wed, 28 Mar 2018 16:52:45 +0200 Subject: [PATCH] update in basic_2 + lemma csx_fsb proved --- .../basic_2/rt_computation/fpbs.ma | 4 ++ .../basic_2/rt_computation/fpbs_fqup.ma | 4 ++ .../basic_2/rt_computation/fpbs_lfpxs.ma | 14 ++++ .../lambdadelta/basic_2/rt_computation/fsb.ma | 3 +- .../basic_2/rt_computation/fsb_csx.ma | 64 +++++++++++-------- .../basic_2/rt_computation/partial.txt | 2 +- 6 files changed, 61 insertions(+), 30 deletions(-) diff --git a/matita/matita/contribs/lambdadelta/basic_2/rt_computation/fpbs.ma b/matita/matita/contribs/lambdadelta/basic_2/rt_computation/fpbs.ma index 74eae9335..82c5eb62a 100644 --- a/matita/matita/contribs/lambdadelta/basic_2/rt_computation/fpbs.ma +++ b/matita/matita/contribs/lambdadelta/basic_2/rt_computation/fpbs.ma @@ -67,6 +67,10 @@ lemma ffdeq_fpbs_trans: ∀h,o,G,G2,L,L2,T,T2. ⦃G, L, T⦄ ≥[h, o] ⦃G2, L2 ∀G1,L1,T1. ⦃G1, L1, T1⦄ ≛[h, o] ⦃G, L, T⦄ → ⦃G1, L1, T1⦄ ≥[h, o] ⦃G2, L2, T2⦄. /3 width=5 by fpbs_strap2, fpbq_ffdeq/ qed-. +lemma tdeq_lfdeq_lfpx_fpbs: ∀h,o,T1,T2. T1 ≛[h, o] T2 → ∀L1,L0. L1 ≛[h, o, T2] L0 → + ∀G,L2. ⦃G, L0⦄ ⊢ ⬈[h, T2] L2 → ⦃G, L1, T1⦄ ≥[h, o] ⦃G, L2, T2⦄. +/4 width=5 by ffdeq_fpbs, fpbs_strap1, fpbq_lfpx, ffdeq_intro_dx/ qed. + (* Basic_2A1: removed theorems 3: fpb_fpbsa_trans fpbs_fpbsa fpbsa_inv_fpbs *) diff --git a/matita/matita/contribs/lambdadelta/basic_2/rt_computation/fpbs_fqup.ma b/matita/matita/contribs/lambdadelta/basic_2/rt_computation/fpbs_fqup.ma index 4cef4f396..ce248aeb1 100644 --- a/matita/matita/contribs/lambdadelta/basic_2/rt_computation/fpbs_fqup.ma +++ b/matita/matita/contribs/lambdadelta/basic_2/rt_computation/fpbs_fqup.ma @@ -24,6 +24,10 @@ lemma tdeq_fpbs_trans: ∀h,o,T1,T. T1 ≛[h, o] T → ∀G1,G2,L1,L2,T2. ⦃G1, L1, T⦄ ≥[h, o] ⦃G2, L2, T2⦄ → ⦃G1, L1, T1⦄ ≥[h, o] ⦃G2, L2, T2⦄. /3 width=5 by ffdeq_fpbs_trans, tdeq_ffdeq/ qed-. +lemma fpbs_tdeq_trans: ∀h,o,G1,G2,L1,L2,T1,T. ⦃G1, L1, T1⦄ ≥[h, o] ⦃G2, L2, T⦄ → + ∀T2. T ≛[h, o] T2 → ⦃G1, L1, T1⦄ ≥[h, o] ⦃G2, L2, T2⦄. +/3 width=5 by fpbs_ffdeq_trans, tdeq_ffdeq/ qed-. + (* Properties with plus-iterated structural successor for closures **********) lemma fqup_fpbs: ∀h,o,G1,G2,L1,L2,T1,T2. ⦃G1, L1, T1⦄ ⊐+ ⦃G2, L2, T2⦄ → diff --git a/matita/matita/contribs/lambdadelta/basic_2/rt_computation/fpbs_lfpxs.ma b/matita/matita/contribs/lambdadelta/basic_2/rt_computation/fpbs_lfpxs.ma index 5a8c400b5..9bccf418d 100644 --- a/matita/matita/contribs/lambdadelta/basic_2/rt_computation/fpbs_lfpxs.ma +++ b/matita/matita/contribs/lambdadelta/basic_2/rt_computation/fpbs_lfpxs.ma @@ -49,6 +49,10 @@ lemma lfpxs_ffdeq_fpbs: ∀h,o,G1,L1,L,T1. ⦃G1, L1⦄ ⊢ ⬈*[h, T1] L → ∀G2,L2,T2. ⦃G1, L, T1⦄ ≛[h, o] ⦃G2, L2, T2⦄ → ⦃G1, L1, T1⦄ ≥[h, o] ⦃G2, L2, T2⦄. /3 width=3 by lfpxs_fpbs_trans, ffdeq_fpbs/ qed. +lemma fpbs_lfpx_trans: ∀h,o,G1,G2,L1,L,T1,T2. ⦃G1, L1, T1⦄ ≥[h, o] ⦃G2, L, T2⦄ → + ∀L2. ⦃G2, L⦄ ⊢ ⬈[h, T2] L2 → ⦃G1, L1, T1⦄ ≥[h, o] ⦃G2, L2, T2⦄. +/3 width=3 by fpbs_lfpxs_trans, lfpx_lfpxs/ qed-. + (* Properties with star-iterated structural successor for closures **********) (* Basic_2A1: uses: fqus_lpxs_fpbs *) @@ -64,6 +68,16 @@ lemma cpxs_fqus_lfpxs_fpbs: ∀h,o,G1,L1,T1,T. ⦃G1, L1⦄ ⊢ T1 ⬈*[h] T → ∀L2.⦃G2, L⦄ ⊢ ⬈*[h, T2] L2 → ⦃G1, L1, T1⦄ ≥[h, o] ⦃G2, L2, T2⦄. /3 width=5 by cpxs_fqus_fpbs, fpbs_lfpxs_trans/ qed. +lemma fpbs_cpxs_tdeq_fqup_lfpx_trans: ∀h,o,G1,G3,L1,L3,T1,T3. ⦃G1, L1, T1⦄ ≥ [h, o] ⦃G3, L3, T3⦄ → + ∀T4. ⦃G3, L3⦄ ⊢ T3 ⬈*[h] T4 → ∀T5. T4 ≛[h, o] T5 → + ∀G2,L4,T2. ⦃G3, L3, T5⦄ ⊐+ ⦃G2, L4, T2⦄ → + ∀L2. ⦃G2, L4⦄ ⊢ ⬈[h, T2] L2 → ⦃G1, L1, T1⦄ ≥ [h, o] ⦃G2, L2, T2⦄. +#h #o #G1 #G3 #L1 #L3 #T1 #T3 #H13 #T4 #HT34 #T5 #HT45 #G2 #L4 #T2 #H34 #L2 #HL42 +@(fpbs_lfpx_trans … HL42) -L2 (**) (* full auto too slow *) +@(fpbs_fqup_trans … H34) -G2 -L4 -T2 +/3 width=3 by fpbs_cpxs_trans, fpbs_tdeq_trans/ +qed-. + (* Advanced properties ******************************************************) lemma fpbs_intro_fstar: ∀h,o,G1,L1,T1,T. ⦃G1, L1⦄ ⊢ T1 ⬈*[h] T → diff --git a/matita/matita/contribs/lambdadelta/basic_2/rt_computation/fsb.ma b/matita/matita/contribs/lambdadelta/basic_2/rt_computation/fsb.ma index 925beb513..62fd4fe10 100644 --- a/matita/matita/contribs/lambdadelta/basic_2/rt_computation/fsb.ma +++ b/matita/matita/contribs/lambdadelta/basic_2/rt_computation/fsb.ma @@ -41,6 +41,7 @@ lemma fsb_ind_alt: ∀h,o. ∀R: relation3 …. ( /4 width=1 by fsb_intro/ qed-. -(* Basic_2A1: removed theorems 5: +(* Basic_2A1: removed theorems 6: fsba_intro fsba_ind_alt fsba_fpbs_trans fsb_fsba fsba_inv_fsb + aaa_fsba *) diff --git a/matita/matita/contribs/lambdadelta/basic_2/rt_computation/fsb_csx.ma b/matita/matita/contribs/lambdadelta/basic_2/rt_computation/fsb_csx.ma index 58325a948..6d25d649b 100644 --- a/matita/matita/contribs/lambdadelta/basic_2/rt_computation/fsb_csx.ma +++ b/matita/matita/contribs/lambdadelta/basic_2/rt_computation/fsb_csx.ma @@ -12,59 +12,67 @@ (* *) (**************************************************************************) -include "basic_2/computation/fpbs_fpb.ma". -include "basic_2/computation/fpbs_fpbs.ma". -include "basic_2/computation/csx_fpbs.ma". -include "basic_2/computation/lsx_csx.ma". -include "basic_2/computation/fsb_alt.ma". +include "basic_2/rt_computation/lfsx_csx.ma". +include "basic_2/rt_computation/fpbs_cpx.ma". +include "basic_2/rt_computation/fpbs_csx.ma". +include "basic_2/rt_computation/fsb_fpbg.ma". -(* "QRST" STRONGLY NORMALIZING CLOSURES *************************************) +(* STRONGLY NORMALIZING CLOSURES FOR PARALLEL RST-TRANSITION ****************) -(* Advanced propreties on context-sensitive extended normalizing terms ******) +(* Inversion lemmas with context-sensitive stringly rt-normalizing terms ****) -lemma csx_fsb_fpbs: ∀h,o,G1,L1,T1. ⦃G1, L1⦄ ⊢ ⬊*[h, o] T1 → - ∀G2,L2,T2. ⦃G1, L1, T1⦄ ≥[h, o] ⦃G2, L2, T2⦄ → ⦥[h, o] ⦃G2, L2, T2⦄. +lemma fsb_inv_csx: ∀h,o,G,L,T. ≥[h, o] 𝐒⦃G, L, T⦄ → ⦃G, L⦄ ⊢ ⬈*[h, o] 𝐒⦃T⦄. +#h #o #G #L #T #H @(fsb_ind_alt … H) -G -L -T /5 width=1 by csx_intro, fpb_cpx/ +qed-. + +(* Propreties with context-sensitive stringly rt-normalizing terms **********) + +lemma csx_fsb_fpbs: ∀h,o,G1,L1,T1. ⦃G1, L1⦄ ⊢ ⬈*[h, o] 𝐒⦃T1⦄ → + ∀G2,L2,T2. ⦃G1, L1, T1⦄ ≥[h, o] ⦃G2, L2, T2⦄ → ≥[h, o] 𝐒⦃G2, L2, T2⦄. #h #o #G1 #L1 #T1 #H @(csx_ind … H) -T1 -#T1 #HT1 #IHc #G2 #L2 #T2 @(fqup_wf_ind … G2 L2 T2) -G2 -L2 -T2 -#G0 #L0 #T0 #IHu #H10 lapply (csx_fpbs_conf … H10) // -HT1 -#HT0 generalize in match IHu; -IHu generalize in match H10; -H10 -@(lsx_ind … (csx_lsx … HT0 0)) -L0 +#T1 #HT1 #IHc #G2 #L2 #T2 @(fqup_wf_ind (Ⓣ) … G2 L2 T2) -G2 -L2 -T2 +#G0 #L0 #T0 #IHu #H10 +lapply (fpbs_csx_conf … H10) // -HT1 #HT0 +generalize in match IHu; -IHu generalize in match H10; -H10 +@(lfsx_ind … (csx_lfsx … HT0)) -L0 #L0 #_ #IHd #H10 #IHu @fsb_intro #G2 #L2 #T2 * -G2 -L2 -T2 [ -IHd -IHc | -IHu -IHd | ] [ /4 width=5 by fpbs_fqup_trans, fqu_fqup/ -| #T2 #HT02 #HnT02 elim (fpbs_cpx_trans_neq … H10 … HT02 HnT02) -T0 +| #T2 #HT02 #HnT02 + elim (fpbs_cpx_tdneq_trans … H10 … HT02 HnT02) -T0 /3 width=4 by/ | #L2 #HL02 #HnL02 @(IHd … HL02 HnL02) -IHd -HnL02 [ -IHu -IHc | ] - [ /3 width=3 by fpbs_lpxs_trans, lpx_lpxs/ - | #G3 #L3 #T3 #H03 #_ elim (lpx_fqup_trans … H03 … HL02) -L2 - #L4 #T4 elim (eq_term_dec T0 T4) [ -IHc | -IHu ] - [ #H destruct /5 width=5 by fsb_fpbs_trans, lpxs_fpbs, fpbs_fqup_trans, lpx_lpxs/ - | #HnT04 #HT04 #H04 #HL43 elim (cpxs_neq_inv_step_sn … HT04 HnT04) -HT04 -HnT04 - #T2 #HT02 #HnT02 #HT24 elim (fpbs_cpx_trans_neq … H10 … HT02 HnT02) -T0 - lapply (fpbs_intro_alt … G3 … L4 … L3 L3 … T3 … HT24 ? ? ?) -HT24 - /3 width=8 by fpbs_trans, lpx_lpxs, fqup_fqus/ (**) (* full auto too slow *) + [ /3 width=3 by fpbs_lfpxs_trans, lfpx_lfpxs/ + | #G3 #L3 #T3 #H03 #_ + elim (lfpx_fqup_trans … H03 … HL02) -L2 #L4 #T4 #HT04 #H43 #HL43 + elim (tdeq_dec h o T0 T4) [ -IHc -HT04 #HT04 | -IHu #HnT04 ] + [ elim (tdeq_fqup_trans … H43 … HT04) -T4 #L2 #T4 #H04 #HT43 #HL24 + /4 width=7 by fsb_fpbs_trans, tdeq_lfdeq_lfpx_fpbs, fpbs_fqup_trans/ + | elim (cpxs_tdneq_fwd_step_sn … HT04 HnT04) -HT04 -HnT04 #T2 #T5 #HT02 #HnT02 #HT25 #HT54 + elim (fpbs_cpx_tdneq_trans … H10 … HT02 HnT02) -T0 #T0 #HT10 #HnT10 #H02 + /3 width=14 by fpbs_cpxs_tdeq_fqup_lfpx_trans/ ] ] ] qed. -lemma csx_fsb: ∀h,o,G,L,T. ⦃G, L⦄ ⊢ ⬊*[h, o] T → ⦥[h, o] ⦃G, L, T⦄. +lemma csx_fsb: ∀h,o,G,L,T. ⦃G, L⦄ ⊢ ⬈*[h, o] 𝐒⦃T⦄ → ≥[h, o] 𝐒⦃G, L, T⦄. /2 width=5 by csx_fsb_fpbs/ qed. (* Advanced eliminators *****************************************************) lemma csx_ind_fpb: ∀h,o. ∀R:relation3 genv lenv term. - (∀G1,L1,T1. ⦃G1, L1⦄ ⊢ ⬊*[h, o] T1 → + (∀G1,L1,T1. ⦃G1, L1⦄ ⊢ ⬈*[h, o] 𝐒⦃T1⦄ → (∀G2,L2,T2. ⦃G1, L1, T1⦄ ≻[h, o] ⦃G2, L2, T2⦄ → R G2 L2 T2) → R G1 L1 T1 ) → - ∀G,L,T. ⦃G, L⦄ ⊢ ⬊*[h, o] T → R G L T. + ∀G,L,T. ⦃G, L⦄ ⊢ ⬈*[h, o] 𝐒⦃T⦄ → R G L T. /4 width=4 by fsb_inv_csx, csx_fsb, fsb_ind_alt/ qed-. lemma csx_ind_fpbg: ∀h,o. ∀R:relation3 genv lenv term. - (∀G1,L1,T1. ⦃G1, L1⦄ ⊢ ⬊*[h, o] T1 → - (∀G2,L2,T2. ⦃G1, L1, T1⦄ >≛[h, o] ⦃G2, L2, T2⦄ → R G2 L2 T2) → + (∀G1,L1,T1. ⦃G1, L1⦄ ⊢ ⬈*[h, o] 𝐒⦃T1⦄ → + (∀G2,L2,T2. ⦃G1, L1, T1⦄ >[h, o] ⦃G2, L2, T2⦄ → R G2 L2 T2) → R G1 L1 T1 ) → - ∀G,L,T. ⦃G, L⦄ ⊢ ⬊*[h, o] T → R G L T. + ∀G,L,T. ⦃G, L⦄ ⊢ ⬈*[h, o] 𝐒⦃T⦄ → R G L T. /4 width=4 by fsb_inv_csx, csx_fsb, fsb_ind_fpbg/ qed-. diff --git a/matita/matita/contribs/lambdadelta/basic_2/rt_computation/partial.txt b/matita/matita/contribs/lambdadelta/basic_2/rt_computation/partial.txt index fc893a1d2..2c46eff5d 100644 --- a/matita/matita/contribs/lambdadelta/basic_2/rt_computation/partial.txt +++ b/matita/matita/contribs/lambdadelta/basic_2/rt_computation/partial.txt @@ -8,4 +8,4 @@ lfsx.ma lfsx_drops.ma lfsx_fqup.ma lfsx_lpx.ma lfsx_lpxs.ma lfsx_lfpxs.ma lfsx_c lsubsx.ma lsubsx_lfsx.ma lsubsx_lsubsx.ma fpbs.ma fpbs_fqup.ma fpbs_fqus.ma fpbs_aaa.ma fpbs_cpx.ma fpbs_fpb.ma fpbs_cpxs.ma fpbs_lpxs.ma fpbs_lfpxs.ma fpbs_csx.ma fpbs_fpbs.ma fpbg.ma fpbg_fqup.ma fpbg_cpxs.ma fpbg_lfpxs.ma fpbg_fpbs.ma fpbg_fpbg.ma -fsb.ma fsb_ffdeq.ma fsb_fpbg.ma +fsb.ma fsb_ffdeq.ma fsb_csx.ma fsb_fpbg.ma -- 2.39.2