X-Git-Url: http://matita.cs.unibo.it/gitweb/?a=blobdiff_plain;f=matita%2Fmatita%2Fcontribs%2Flambdadelta%2Fbasic_2%2Frt_computation%2Ffpbs_lpxs.ma;h=c5ad6426a47db9cc6a83c27c86b65e5d764fd38a;hb=4173283e148199871d787c53c0301891deb90713;hp=3a67b6f4969b0c0a2c1aca437923bda81b4f30c0;hpb=222044da28742b24584549ba86b1805a87def070;p=helm.git diff --git a/matita/matita/contribs/lambdadelta/basic_2/rt_computation/fpbs_lpxs.ma b/matita/matita/contribs/lambdadelta/basic_2/rt_computation/fpbs_lpxs.ma index 3a67b6f49..c5ad6426a 100644 --- a/matita/matita/contribs/lambdadelta/basic_2/rt_computation/fpbs_lpxs.ma +++ b/matita/matita/contribs/lambdadelta/basic_2/rt_computation/fpbs_lpxs.ma @@ -12,8 +12,8 @@ (* *) (**************************************************************************) -include "basic_2/static/fdeq_fqus.ma". -include "basic_2/static/fdeq_fdeq.ma". +include "static_2/static/fdeq_fqus.ma". +include "static_2/static/fdeq_fdeq.ma". include "basic_2/rt_computation/cpxs_fqus.ma". include "basic_2/rt_computation/cpxs_fdeq.ma". include "basic_2/rt_computation/lpxs_fdeq.ma". @@ -23,50 +23,50 @@ include "basic_2/rt_computation/fpbs_cpxs.ma". (* Properties with unbound rt-computation on full local environments *******) -lemma lpxs_fpbs: ∀h,o,G,L1,L2,T. ⦃G, L1⦄ ⊢ ⬈*[h] L2 → ⦃G, L1, T⦄ ≥[h, o] ⦃G, L2, T⦄. -#h #o #G #L1 #L2 #T #H @(lpxs_ind_dx … H) -L2 +lemma lpxs_fpbs: ∀h,G,L1,L2,T. ⦃G, L1⦄ ⊢ ⬈*[h] L2 → ⦃G, L1, T⦄ ≥[h] ⦃G, L2, T⦄. +#h #G #L1 #L2 #T #H @(lpxs_ind_dx … H) -L2 /3 width=5 by fpbq_lpx, fpbs_strap1/ qed. -lemma fpbs_lpxs_trans: ∀h,o,G1,G2,L1,L,T1,T2. ⦃G1, L1, T1⦄ ≥[h, o] ⦃G2, L, T2⦄ → - ∀L2. ⦃G2, L⦄ ⊢ ⬈*[h] L2 → ⦃G1, L1, T1⦄ ≥[h, o] ⦃G2, L2, T2⦄. -#h #o #G1 #G2 #L1 #L #T1 #T2 #H1 #L2 #H @(lpxs_ind_dx … H) -L2 +lemma fpbs_lpxs_trans: ∀h,G1,G2,L1,L,T1,T2. ⦃G1, L1, T1⦄ ≥[h] ⦃G2, L, T2⦄ → + ∀L2. ⦃G2, L⦄ ⊢ ⬈*[h] L2 → ⦃G1, L1, T1⦄ ≥[h] ⦃G2, L2, T2⦄. +#h #G1 #G2 #L1 #L #T1 #T2 #H1 #L2 #H @(lpxs_ind_dx … H) -L2 /3 width=5 by fpbs_strap1, fpbq_lpx/ qed-. -lemma lpxs_fpbs_trans: ∀h,o,G1,G2,L,L2,T1,T2. ⦃G1, L, T1⦄ ≥[h, o] ⦃G2, L2, T2⦄ → - ∀L1. ⦃G1, L1⦄ ⊢ ⬈*[h] L → ⦃G1, L1, T1⦄ ≥[h, o] ⦃G2, L2, T2⦄. -#h #o #G1 #G2 #L #L2 #T1 #T2 #H1 #L1 #H @(lpxs_ind_sn … H) -L1 +lemma lpxs_fpbs_trans: ∀h,G1,G2,L,L2,T1,T2. ⦃G1, L, T1⦄ ≥[h] ⦃G2, L2, T2⦄ → + ∀L1. ⦃G1, L1⦄ ⊢ ⬈*[h] L → ⦃G1, L1, T1⦄ ≥[h] ⦃G2, L2, T2⦄. +#h #G1 #G2 #L #L2 #T1 #T2 #H1 #L1 #H @(lpxs_ind_sn … H) -L1 /3 width=5 by fpbs_strap2, fpbq_lpx/ qed-. (* Basic_2A1: uses: lpxs_lleq_fpbs *) -lemma lpxs_fdeq_fpbs: ∀h,o,G1,L1,L,T1. ⦃G1, L1⦄ ⊢ ⬈*[h] L → - ∀G2,L2,T2. ⦃G1, L, T1⦄ ≛[h, o] ⦃G2, L2, T2⦄ → ⦃G1, L1, T1⦄ ≥[h, o] ⦃G2, L2, T2⦄. +lemma lpxs_fdeq_fpbs: ∀h,G1,L1,L,T1. ⦃G1, L1⦄ ⊢ ⬈*[h] L → + ∀G2,L2,T2. ⦃G1, L, T1⦄ ≛ ⦃G2, L2, T2⦄ → ⦃G1, L1, T1⦄ ≥[h] ⦃G2, L2, T2⦄. /3 width=3 by lpxs_fpbs_trans, fdeq_fpbs/ qed. -lemma fpbs_lpx_trans: ∀h,o,G1,G2,L1,L,T1,T2. ⦃G1, L1, T1⦄ ≥[h, o] ⦃G2, L, T2⦄ → - ∀L2. ⦃G2, L⦄ ⊢ ⬈[h] L2 → ⦃G1, L1, T1⦄ ≥[h, o] ⦃G2, L2, T2⦄. +lemma fpbs_lpx_trans: ∀h,G1,G2,L1,L,T1,T2. ⦃G1, L1, T1⦄ ≥[h] ⦃G2, L, T2⦄ → + ∀L2. ⦃G2, L⦄ ⊢ ⬈[h] L2 → ⦃G1, L1, T1⦄ ≥[h] ⦃G2, L2, T2⦄. /3 width=3 by fpbs_lpxs_trans, lpx_lpxs/ qed-. (* Properties with star-iterated structural successor for closures **********) -lemma fqus_lpxs_fpbs: ∀h,o,G1,G2,L1,L,T1,T2. ⦃G1, L1, T1⦄ ⊐* ⦃G2, L, T2⦄ → - ∀L2. ⦃G2, L⦄ ⊢ ⬈*[h] L2 → ⦃G1, L1, T1⦄ ≥[h, o] ⦃G2, L2, T2⦄. +lemma fqus_lpxs_fpbs: ∀h,G1,G2,L1,L,T1,T2. ⦃G1, L1, T1⦄ ⊐* ⦃G2, L, T2⦄ → + ∀L2. ⦃G2, L⦄ ⊢ ⬈*[h] L2 → ⦃G1, L1, T1⦄ ≥[h] ⦃G2, L2, T2⦄. /3 width=3 by fpbs_lpxs_trans, fqus_fpbs/ qed. (* Properties with unbound context-sensitive parallel rt-computation ********) -lemma cpxs_fqus_lpxs_fpbs: ∀h,o,G1,L1,T1,T. ⦃G1, L1⦄ ⊢ T1 ⬈*[h] T → +lemma cpxs_fqus_lpxs_fpbs: ∀h,G1,L1,T1,T. ⦃G1, L1⦄ ⊢ T1 ⬈*[h] T → ∀G2,L,T2. ⦃G1, L1, T⦄ ⊐* ⦃G2, L, T2⦄ → - ∀L2.⦃G2, L⦄ ⊢ ⬈*[h] L2 → ⦃G1, L1, T1⦄ ≥[h, o] ⦃G2, L2, T2⦄. + ∀L2.⦃G2, L⦄ ⊢ ⬈*[h] L2 → ⦃G1, L1, T1⦄ ≥[h] ⦃G2, L2, T2⦄. /3 width=5 by cpxs_fqus_fpbs, fpbs_lpxs_trans/ qed. -lemma fpbs_cpxs_tdeq_fqup_lpx_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 → +lemma fpbs_cpxs_tdeq_fqup_lpx_trans: ∀h,G1,G3,L1,L3,T1,T3. ⦃G1, L1, T1⦄ ≥ [h] ⦃G3, L3, T3⦄ → + ∀T4. ⦃G3, L3⦄ ⊢ T3 ⬈*[h] T4 → ∀T5. T4 ≛ T5 → ∀G2,L4,T2. ⦃G3, L3, T5⦄ ⊐+ ⦃G2, L4, T2⦄ → - ∀L2. ⦃G2, L4⦄ ⊢ ⬈[h] 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 + ∀L2. ⦃G2, L4⦄ ⊢ ⬈[h] L2 → ⦃G1, L1, T1⦄ ≥ [h] ⦃G2, L2, T2⦄. +#h #G1 #G3 #L1 #L3 #T1 #T3 #H13 #T4 #HT34 #T5 #HT45 #G2 #L4 #T2 #H34 #L2 #HL42 @(fpbs_lpx_trans … HL42) -L2 (**) (* full auto too slow *) @(fpbs_fqup_trans … H34) -G2 -L4 -T2 /3 width=3 by fpbs_cpxs_trans, fpbs_tdeq_trans/ @@ -75,19 +75,19 @@ qed-. (* Advanced properties ******************************************************) (* Basic_2A1: uses: fpbs_intro_alt *) -lemma fpbs_intro_star: ∀h,o,G1,L1,T1,T. ⦃G1, L1⦄ ⊢ T1 ⬈*[h] T → +lemma fpbs_intro_star: ∀h,G1,L1,T1,T. ⦃G1, L1⦄ ⊢ T1 ⬈*[h] T → ∀G,L,T0. ⦃G1, L1, T⦄ ⊐* ⦃G, L, T0⦄ → ∀L0. ⦃G, L⦄ ⊢ ⬈*[h] L0 → - ∀G2,L2,T2. ⦃G, L0, T0⦄ ≛[h, o] ⦃G2, L2, T2⦄ → ⦃G1, L1, T1⦄ ≥[h, o] ⦃G2, L2, T2⦄ . + ∀G2,L2,T2. ⦃G, L0, T0⦄ ≛ ⦃G2, L2, T2⦄ → ⦃G1, L1, T1⦄ ≥[h] ⦃G2, L2, T2⦄ . /3 width=5 by cpxs_fqus_lpxs_fpbs, fpbs_strap1, fpbq_fdeq/ qed. (* Advanced inversion lemmas *************************************************) (* Basic_2A1: uses: fpbs_inv_alt *) -lemma fpbs_inv_star: ∀h,o,G1,G2,L1,L2,T1,T2. ⦃G1, L1, T1⦄ ≥[h, o] ⦃G2, L2, T2⦄ → +lemma fpbs_inv_star: ∀h,G1,G2,L1,L2,T1,T2. ⦃G1, L1, T1⦄ ≥[h] ⦃G2, L2, T2⦄ → ∃∃G,L,L0,T,T0. ⦃G1, L1⦄ ⊢ T1 ⬈*[h] T & ⦃G1, L1, T⦄ ⊐* ⦃G, L, T0⦄ - & ⦃G, L⦄ ⊢ ⬈*[h] L0 & ⦃G, L0, T0⦄ ≛[h, o] ⦃G2, L2, T2⦄. -#h #o #G1 #G2 #L1 #L2 #T1 #T2 #H @(fpbs_ind_dx … H) -G1 -L1 -T1 + & ⦃G, L⦄ ⊢ ⬈*[h] L0 & ⦃G, L0, T0⦄ ≛ ⦃G2, L2, T2⦄. +#h #G1 #G2 #L1 #L2 #T1 #T2 #H @(fpbs_ind_dx … H) -G1 -L1 -T1 [ /2 width=9 by ex4_5_intro/ | #G1 #G0 #L1 #L0 #T1 #T0 * -G0 -L0 -T0 [ #G0 #L0 #T0 #H10 #_ * #G3 #L3 #L4 #T3 #T4 #HT03 #H34 #HL34 #H42