From: Ferruccio Guidi Date: Thu, 26 Oct 2017 18:21:59 +0000 (+0000) Subject: - cpxs completed X-Git-Tag: make_still_working~419 X-Git-Url: http://matita.cs.unibo.it/gitweb/?p=helm.git;a=commitdiff_plain;h=04fd7eb3c5a819f6ae00dd9033493c0aa434d241 - cpxs completed - changed colors in sunnary tables for web site --- diff --git a/matita/matita/contribs/lambdadelta/Makefile b/matita/matita/contribs/lambdadelta/Makefile index 7065d3a1f..e0817c219 100644 --- a/matita/matita/contribs/lambdadelta/Makefile +++ b/matita/matita/contribs/lambdadelta/Makefile @@ -207,12 +207,12 @@ define SUMMARY_TEMPLATE @printf ' class "gray" [ "category"\n' >> $$@ @printf ' [ "objects" * ]\n' >> $$@ @printf ' ]\n' >> $$@ - @printf ' class "cyan" [ "sizes"\n' >> $$@ + @printf ' class "water" [ "sizes"\n' >> $$@ @printf ' [ "files" "$$(S1)" ]\n' >> $$@ @printf ' [ "characters" "$$(S2)" ]\n' >> $$@ @printf ' [ "nodes" "$$(S4)" ]\n' >> $$@ @printf ' ]\n' >> $$@ - @printf ' class "green" [ "propositions"\n' >> $$@ + @printf ' class "grass" [ "propositions"\n' >> $$@ @printf ' [ "theorems" "$$(P1)" ]\n' >> $$@ @printf ' [ "lemmas" "$$(P2)" ]\n' >> $$@ @printf ' [ "total" "$$(P3)" ]\n' >> $$@ diff --git a/matita/matita/contribs/lambdadelta/basic_2/etc/lstas/lstas_cpxs.etc b/matita/matita/contribs/lambdadelta/basic_2/etc/lstas/lstas_cpxs.etc new file mode 100644 index 000000000..088b4daae --- /dev/null +++ b/matita/matita/contribs/lambdadelta/basic_2/etc/lstas/lstas_cpxs.etc @@ -0,0 +1,45 @@ +(**************************************************************************) +(* ___ *) +(* ||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 *) +(* *) +(**************************************************************************) + +(* Advanced properties ******************************************************) + +lemma lstas_cpxs: ∀h,o,G,L,T1,T2,d2. ⦃G, L⦄ ⊢ T1 •*[h, d2] T2 → + ∀d1. ⦃G, L⦄ ⊢ T1 ▪[h, o] d1 → d2 ≤ d1 → ⦃G, L⦄ ⊢ T1 ⬈*[h, o] T2. +#h #o #G #L #T1 #T2 #d2 #H elim H -G -L -T1 -T2 -d2 // +[ /3 width=3 by cpxs_sort, da_inv_sort/ +| #G #L #K #V1 #V2 #W2 #i #d2 #HLK #_ #HVW2 #IHV12 #d1 #H #Hd21 + elim (da_inv_lref … H) -H * #K0 #V0 [| #d0 ] #HLK0 + lapply (drop_mono … HLK0 … HLK) -HLK0 #H destruct /3 width=7 by cpxs_delta/ +| #G #L #K #V1 #V2 #W2 #i #d2 #HLK #_ #HVW2 #IHV12 #d1 #H #Hd21 + elim (da_inv_lref … H) -H * #K0 #V0 [| #d0 ] #HLK0 + lapply (drop_mono … HLK0 … HLK) -HLK0 #H destruct + #HV1 #H destruct lapply (le_plus_to_le_c … Hd21) -Hd21 + /3 width=7 by cpxs_delta/ +| /4 width=3 by cpxs_bind_dx, da_inv_bind/ +| /4 width=3 by cpxs_flat_dx, da_inv_flat/ +| /4 width=3 by cpxs_eps, da_inv_flat/ +] +qed. + +lemma fquq_lstas_trans: ∀h,o,G1,G2,L1,L2,T1,T2. ⦃G1, L1, T1⦄ ⊐⸮ ⦃G2, L2, T2⦄ → + ∀U2,d1. ⦃G2, L2⦄ ⊢ T2 •*[h, d1] U2 → + ∀d2. ⦃G2, L2⦄ ⊢ T2 ▪[h, o] d2 → d1 ≤ d2 → + ∃∃U1. ⦃G1, L1⦄ ⊢ T1 ⬈*[h, o] U1 & ⦃G1, L1, U1⦄ ⊐⸮ ⦃G2, L2, U2⦄. +/3 width=5 by fquq_cpxs_trans, lstas_cpxs/ qed-. + +lemma fqus_lstas_trans: ∀h,o,G1,G2,L1,L2,T1,T2. ⦃G1, L1, T1⦄ ⊐* ⦃G2, L2, T2⦄ → + ∀U2,d1. ⦃G2, L2⦄ ⊢ T2 •*[h, d1] U2 → + ∀d2. ⦃G2, L2⦄ ⊢ T2 ▪[h, o] d2 → d1 ≤ d2 → + ∃∃U1. ⦃G1, L1⦄ ⊢ T1 ⬈*[h, o] U1 & ⦃G1, L1, U1⦄ ⊐* ⦃G2, L2, U2⦄. +/3 width=6 by fqus_cpxs_trans, lstas_cpxs/ qed-. diff --git a/matita/matita/contribs/lambdadelta/basic_2/rt_computation/cpxs_fqus.ma b/matita/matita/contribs/lambdadelta/basic_2/rt_computation/cpxs_fqus.ma index 82e21018e..9ecbc31c6 100644 --- a/matita/matita/contribs/lambdadelta/basic_2/rt_computation/cpxs_fqus.ma +++ b/matita/matita/contribs/lambdadelta/basic_2/rt_computation/cpxs_fqus.ma @@ -1,132 +1,118 @@ -include "basic_2/computation/cpxs_lift.ma". -include "basic_2/multiple/fqus_fqus.ma". +(**************************************************************************) +(* ___ *) +(* ||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 *) +(* *) +(**************************************************************************) -(* Advanced properties ******************************************************) +(* UNCOUNTED CONTEXT-SENSITIVE PARALLEL RT-COMPUTATION FOR TERMS ************) -lemma lstas_cpxs: ∀h,o,G,L,T1,T2,d2. ⦃G, L⦄ ⊢ T1 •*[h, d2] T2 → - ∀d1. ⦃G, L⦄ ⊢ T1 ▪[h, o] d1 → d2 ≤ d1 → ⦃G, L⦄ ⊢ T1 ⬈*[h, o] T2. -#h #o #G #L #T1 #T2 #d2 #H elim H -G -L -T1 -T2 -d2 // -[ /3 width=3 by cpxs_sort, da_inv_sort/ -| #G #L #K #V1 #V2 #W2 #i #d2 #HLK #_ #HVW2 #IHV12 #d1 #H #Hd21 - elim (da_inv_lref … H) -H * #K0 #V0 [| #d0 ] #HLK0 - lapply (drop_mono … HLK0 … HLK) -HLK0 #H destruct /3 width=7 by cpxs_delta/ -| #G #L #K #V1 #V2 #W2 #i #d2 #HLK #_ #HVW2 #IHV12 #d1 #H #Hd21 - elim (da_inv_lref … H) -H * #K0 #V0 [| #d0 ] #HLK0 - lapply (drop_mono … HLK0 … HLK) -HLK0 #H destruct - #HV1 #H destruct lapply (le_plus_to_le_c … Hd21) -Hd21 - /3 width=7 by cpxs_delta/ -| /4 width=3 by cpxs_bind_dx, da_inv_bind/ -| /4 width=3 by cpxs_flat_dx, da_inv_flat/ -| /4 width=3 by cpxs_eps, da_inv_flat/ -] -qed. +include "basic_2/rt_transition/cpx_fqus.ma". +include "basic_2/rt_computation/cpxs_drops.ma". +include "basic_2/rt_computation/cpxs_lsubr.ma". +include "basic_2/rt_computation/cpxs_cpxs.ma". (* Properties on supclosure *************************************************) -lemma fqu_cpxs_trans: ∀h,o,G1,G2,L1,L2,T2,U2. ⦃G2, L2⦄ ⊢ T2 ⬈*[h, o] U2 → - ∀T1. ⦃G1, L1, T1⦄ ⊐ ⦃G2, L2, T2⦄ → - ∃∃U1. ⦃G1, L1⦄ ⊢ T1 ⬈*[h, o] U1 & ⦃G1, L1, U1⦄ ⊐ ⦃G2, L2, U2⦄. -#h #o #G1 #G2 #L1 #L2 #T2 #U2 #H @(cpxs_ind_dx … H) -T2 /2 width=3 by ex2_intro/ +lemma fqu_cpxs_trans: ∀h,b,G1,G2,L1,L2,T2,U2. ⦃G2, L2⦄ ⊢ T2 ⬈*[h] U2 → + ∀T1. ⦃G1, L1, T1⦄ ⊐[b] ⦃G2, L2, T2⦄ → + ∃∃U1. ⦃G1, L1⦄ ⊢ T1 ⬈*[h] U1 & ⦃G1, L1, U1⦄ ⊐[b] ⦃G2, L2, U2⦄. +#h #b #G1 #G2 #L1 #L2 #T2 #U2 #H @(cpxs_ind_dx … H) -T2 /2 width=3 by ex2_intro/ #T #T2 #HT2 #_ #IHTU2 #T1 #HT1 elim (fqu_cpx_trans … HT1 … HT2) -T #T #HT1 #HT2 elim (IHTU2 … HT2) -T2 /3 width=3 by cpxs_strap2, ex2_intro/ qed-. -lemma fquq_cpxs_trans: ∀h,o,G1,G2,L1,L2,T2,U2. ⦃G2, L2⦄ ⊢ T2 ⬈*[h, o] U2 → - ∀T1. ⦃G1, L1, T1⦄ ⊐⸮ ⦃G2, L2, T2⦄ → - ∃∃U1. ⦃G1, L1⦄ ⊢ T1 ⬈*[h, o] U1 & ⦃G1, L1, U1⦄ ⊐⸮ ⦃G2, L2, U2⦄. -#h #o #G1 #G2 #L1 #L2 #T2 #U2 #HTU2 #T1 #H elim (fquq_inv_gen … H) -H -[ #HT12 elim (fqu_cpxs_trans … HTU2 … HT12) /3 width=3 by fqu_fquq, ex2_intro/ -| * #H1 #H2 #H3 destruct /2 width=3 by ex2_intro/ -] +lemma fquq_cpxs_trans: ∀h,b,G1,G2,L1,L2,T2,U2. ⦃G2, L2⦄ ⊢ T2 ⬈*[h] U2 → + ∀T1. ⦃G1, L1, T1⦄ ⊐⸮[b] ⦃G2, L2, T2⦄ → + ∃∃U1. ⦃G1, L1⦄ ⊢ T1 ⬈*[h] U1 & ⦃G1, L1, U1⦄ ⊐⸮[b] ⦃G2, L2, U2⦄. +#h #b #G1 #G2 #L1 #L2 #T2 #U2 #H @(cpxs_ind_dx … H) -T2 /2 width=3 by ex2_intro/ +#T #T2 #HT2 #_ #IHTU2 #T1 #HT1 elim (fquq_cpx_trans … HT1 … HT2) -T +#T #HT1 #HT2 elim (IHTU2 … HT2) -T2 /3 width=3 by cpxs_strap2, ex2_intro/ qed-. -lemma fquq_lstas_trans: ∀h,o,G1,G2,L1,L2,T1,T2. ⦃G1, L1, T1⦄ ⊐⸮ ⦃G2, L2, T2⦄ → - ∀U2,d1. ⦃G2, L2⦄ ⊢ T2 •*[h, d1] U2 → - ∀d2. ⦃G2, L2⦄ ⊢ T2 ▪[h, o] d2 → d1 ≤ d2 → - ∃∃U1. ⦃G1, L1⦄ ⊢ T1 ⬈*[h, o] U1 & ⦃G1, L1, U1⦄ ⊐⸮ ⦃G2, L2, U2⦄. -/3 width=5 by fquq_cpxs_trans, lstas_cpxs/ qed-. - -lemma fqup_cpxs_trans: ∀h,o,G1,G2,L1,L2,T2,U2. ⦃G2, L2⦄ ⊢ T2 ⬈*[h, o] U2 → - ∀T1. ⦃G1, L1, T1⦄ ⊐+ ⦃G2, L2, T2⦄ → - ∃∃U1. ⦃G1, L1⦄ ⊢ T1 ⬈*[h, o] U1 & ⦃G1, L1, U1⦄ ⊐+ ⦃G2, L2, U2⦄. -#h #o #G1 #G2 #L1 #L2 #T2 #U2 #H @(cpxs_ind_dx … H) -T2 /2 width=3 by ex2_intro/ +lemma fqup_cpxs_trans: ∀h,b,G1,G2,L1,L2,T2,U2. ⦃G2, L2⦄ ⊢ T2 ⬈*[h] U2 → + ∀T1. ⦃G1, L1, T1⦄ ⊐+[b] ⦃G2, L2, T2⦄ → + ∃∃U1. ⦃G1, L1⦄ ⊢ T1 ⬈*[h] U1 & ⦃G1, L1, U1⦄ ⊐+[b] ⦃G2, L2, U2⦄. +#h #b #G1 #G2 #L1 #L2 #T2 #U2 #H @(cpxs_ind_dx … H) -T2 /2 width=3 by ex2_intro/ #T #T2 #HT2 #_ #IHTU2 #T1 #HT1 elim (fqup_cpx_trans … HT1 … HT2) -T #U1 #HTU1 #H2 elim (IHTU2 … H2) -T2 /3 width=3 by cpxs_strap2, ex2_intro/ qed-. -lemma fqus_cpxs_trans: ∀h,o,G1,G2,L1,L2,T2,U2. ⦃G2, L2⦄ ⊢ T2 ⬈*[h, o] U2 → - ∀T1. ⦃G1, L1, T1⦄ ⊐* ⦃G2, L2, T2⦄ → - ∃∃U1. ⦃G1, L1⦄ ⊢ T1 ⬈*[h, o] U1 & ⦃G1, L1, U1⦄ ⊐* ⦃G2, L2, U2⦄. -#h #o #G1 #G2 #L1 #L2 #T2 #U2 #HTU2 #T1 #H elim (fqus_inv_gen … H) -H -[ #HT12 elim (fqup_cpxs_trans … HTU2 … HT12) /3 width=3 by fqup_fqus, ex2_intro/ -| * #H1 #H2 #H3 destruct /2 width=3 by ex2_intro/ -] +lemma fqus_cpxs_trans: ∀h,b,G1,G2,L1,L2,T2,U2. ⦃G2, L2⦄ ⊢ T2 ⬈*[h] U2 → + ∀T1. ⦃G1, L1, T1⦄ ⊐*[b] ⦃G2, L2, T2⦄ → + ∃∃U1. ⦃G1, L1⦄ ⊢ T1 ⬈*[h] U1 & ⦃G1, L1, U1⦄ ⊐*[b] ⦃G2, L2, U2⦄. +#h #b #G1 #G2 #L1 #L2 #T2 #U2 #H @(cpxs_ind_dx … H) -T2 /2 width=3 by ex2_intro/ +#T #T2 #HT2 #_ #IHTU2 #T1 #HT1 elim (fqus_cpx_trans … HT1 … HT2) -T +#U1 #HTU1 #H2 elim (IHTU2 … H2) -T2 /3 width=3 by cpxs_strap2, ex2_intro/ qed-. -lemma fqus_lstas_trans: ∀h,o,G1,G2,L1,L2,T1,T2. ⦃G1, L1, T1⦄ ⊐* ⦃G2, L2, T2⦄ → - ∀U2,d1. ⦃G2, L2⦄ ⊢ T2 •*[h, d1] U2 → - ∀d2. ⦃G2, L2⦄ ⊢ T2 ▪[h, o] d2 → d1 ≤ d2 → - ∃∃U1. ⦃G1, L1⦄ ⊢ T1 ⬈*[h, o] U1 & ⦃G1, L1, U1⦄ ⊐* ⦃G2, L2, U2⦄. -/3 width=6 by fqus_cpxs_trans, lstas_cpxs/ qed-. - -(* Properties on supclosure *************************************************) - -lemma fqu_cpxs_trans_neq: ∀h,o,G1,G2,L1,L2,T1,T2. ⦃G1, L1, T1⦄ ⊐ ⦃G2, L2, T2⦄ → - ∀U2. ⦃G2, L2⦄ ⊢ T2 ⬈*[h, o] U2 → (T2 = U2 → ⊥) → - ∃∃U1. ⦃G1, L1⦄ ⊢ T1 ⬈*[h, o] U1 & T1 = U1 → ⊥ & ⦃G1, L1, U1⦄ ⊐ ⦃G2, L2, U2⦄. -#h #o #G1 #G2 #L1 #L2 #T1 #T2 #H elim H -G1 -G2 -L1 -L2 -T1 -T2 -[ #I #G #L #V1 #V2 #HV12 #_ elim (lift_total V2 0 1) +(* Note: a proof based on fqu_cpx_trans_ntdeq might exist *) +lemma fqu_cpxs_trans_ntdeq: ∀h,o,b,G1,G2,L1,L2,T1,T2. ⦃G1, L1, T1⦄ ⊐[b] ⦃G2, L2, T2⦄ → + ∀U2. ⦃G2, L2⦄ ⊢ T2 ⬈*[h] U2 → (T2 ≡[h, o] U2 → ⊥) → + ∃∃U1. ⦃G1, L1⦄ ⊢ T1 ⬈*[h] U1 & T1 ≡[h, o] U1 → ⊥ & ⦃G1, L1, U1⦄ ⊐[b] ⦃G2, L2, U2⦄. +#h #o #b #G1 #G2 #L1 #L2 #T1 #T2 #H elim H -G1 -G2 -L1 -L2 -T1 -T2 +[ #I #G #L #V1 #V2 #HV12 #_ elim (lifts_total V2 𝐔❴1❵) #U2 #HVU2 @(ex3_intro … U2) - [1,3: /3 width=7 by fqu_drop, cpxs_delta, drop_pair, drop_drop/ - | #H destruct - lapply (lift_inv_lref2_be … HVU2 ? ?) -HVU2 // + [1,3: /3 width=7 by cpxs_delta, fqu_drop/ + | #H lapply (tdeq_inv_lref1 … H) -H + #H destruct /2 width=5 by lifts_inv_lref2_uni_lt/ ] -| #I #G #L #V1 #T #V2 #HV12 #H @(ex3_intro … (②{I}V2.T)) +| #I #G #L #V1 #T #V2 #HV12 #H0 @(ex3_intro … (②{I}V2.T)) [1,3: /2 width=4 by fqu_pair_sn, cpxs_pair_sn/ - | #H0 destruct /2 width=1 by/ + | #H elim (tdeq_inv_pair … H) -H /2 width=1 by/ ] -| #a #I #G #L #V #T1 #T2 #HT12 #H @(ex3_intro … (ⓑ{a,I}V.T2)) +| #p #I #G #L #V #T1 #T2 #HT12 #H0 @(ex3_intro … (ⓑ{p,I}V.T2)) [1,3: /2 width=4 by fqu_bind_dx, cpxs_bind/ - | #H0 destruct /2 width=1 by/ + | #H elim (tdeq_inv_pair … H) -H /2 width=1 by/ + ] +| #p #I #G #L #V #T1 #Hb #T2 #HT12 #H0 @(ex3_intro … (ⓑ{p,I}V.T2)) + [1,3: /4 width=4 by lsubr_cpxs_trans, cpxs_bind, lsubr_unit, fqu_clear/ + | #H elim (tdeq_inv_pair … H) -H /2 width=1 by/ ] -| #I #G #L #V #T1 #T2 #HT12 #H @(ex3_intro … (ⓕ{I}V.T2)) +| #I #G #L #V #T1 #T2 #HT12 #H0 @(ex3_intro … (ⓕ{I}V.T2)) [1,3: /2 width=4 by fqu_flat_dx, cpxs_flat/ - | #H0 destruct /2 width=1 by/ + | #H elim (tdeq_inv_pair … H) -H /2 width=1 by/ ] -| #G #L #K #T1 #U1 #k #HLK #HTU1 #T2 #HT12 #H elim (lift_total T2 0 (k+1)) - #U2 #HTU2 @(ex3_intro … U2) - [1,3: /2 width=10 by cpxs_lift, fqu_drop/ - | #H0 destruct /3 width=5 by lift_inj/ +| #I #G #L #T1 #U1 #HTU1 #T2 #HT12 #H0 + elim (cpxs_lifts_sn … HT12 (Ⓣ) … (L.ⓘ{I}) … HTU1) -HT12 + /4 width=6 by fqu_drop, drops_refl, drops_drop, tdeq_inv_lifts_bi, ex3_intro/ ] qed-. -lemma fquq_cpxs_trans_neq: ∀h,o,G1,G2,L1,L2,T1,T2. ⦃G1, L1, T1⦄ ⊐⸮ ⦃G2, L2, T2⦄ → - ∀U2. ⦃G2, L2⦄ ⊢ T2 ⬈*[h, o] U2 → (T2 = U2 → ⊥) → - ∃∃U1. ⦃G1, L1⦄ ⊢ T1 ⬈*[h, o] U1 & T1 = U1 → ⊥ & ⦃G1, L1, U1⦄ ⊐⸮ ⦃G2, L2, U2⦄. -#h #o #G1 #G2 #L1 #L2 #T1 #T2 #H12 #U2 #HTU2 #H elim (fquq_inv_gen … H12) -H12 -[ #H12 elim (fqu_cpxs_trans_neq … H12 … HTU2 H) -T2 +lemma fquq_cpxs_trans_ntdeq: ∀h,o,b,G1,G2,L1,L2,T1,T2. ⦃G1, L1, T1⦄ ⊐⸮[b] ⦃G2, L2, T2⦄ → + ∀U2. ⦃G2, L2⦄ ⊢ T2 ⬈*[h] U2 → (T2 ≡[h, o] U2 → ⊥) → + ∃∃U1. ⦃G1, L1⦄ ⊢ T1 ⬈*[h] U1 & T1 ≡[h, o] U1 → ⊥ & ⦃G1, L1, U1⦄ ⊐⸮[b] ⦃G2, L2, U2⦄. +#h #o #b #G1 #G2 #L1 #L2 #T1 #T2 #H12 elim H12 -H12 +[ #H12 #U2 #HTU2 #H elim (fqu_cpxs_trans_ntdeq … H12 … HTU2 H) -T2 /3 width=4 by fqu_fquq, ex3_intro/ | * #HG #HL #HT destruct /3 width=4 by ex3_intro/ ] qed-. -lemma fqup_cpxs_trans_neq: ∀h,o,G1,G2,L1,L2,T1,T2. ⦃G1, L1, T1⦄ ⊐+ ⦃G2, L2, T2⦄ → - ∀U2. ⦃G2, L2⦄ ⊢ T2 ⬈*[h, o] U2 → (T2 = U2 → ⊥) → - ∃∃U1. ⦃G1, L1⦄ ⊢ T1 ⬈*[h, o] U1 & T1 = U1 → ⊥ & ⦃G1, L1, U1⦄ ⊐+ ⦃G2, L2, U2⦄. -#h #o #G1 #G2 #L1 #L2 #T1 #T2 #H @(fqup_ind_dx … H) -G1 -L1 -T1 -[ #G1 #L1 #T1 #H12 #U2 #HTU2 #H elim (fqu_cpxs_trans_neq … H12 … HTU2 H) -T2 +lemma fqup_cpxs_trans_ntdeq: ∀h,o,b,G1,G2,L1,L2,T1,T2. ⦃G1, L1, T1⦄ ⊐+[b] ⦃G2, L2, T2⦄ → + ∀U2. ⦃G2, L2⦄ ⊢ T2 ⬈*[h] U2 → (T2 ≡[h, o] U2 → ⊥) → + ∃∃U1. ⦃G1, L1⦄ ⊢ T1 ⬈*[h] U1 & T1 ≡[h, o] U1 → ⊥ & ⦃G1, L1, U1⦄ ⊐+[b] ⦃G2, L2, U2⦄. +#h #o #b #G1 #G2 #L1 #L2 #T1 #T2 #H @(fqup_ind_dx … H) -G1 -L1 -T1 +[ #G1 #L1 #T1 #H12 #U2 #HTU2 #H elim (fqu_cpxs_trans_ntdeq … H12 … HTU2 H) -T2 /3 width=4 by fqu_fqup, ex3_intro/ | #G #G1 #L #L1 #T #T1 #H1 #_ #IH12 #U2 #HTU2 #H elim (IH12 … HTU2 H) -T2 - #U1 #HTU1 #H #H12 elim (fqu_cpxs_trans_neq … H1 … HTU1 H) -T1 + #U1 #HTU1 #H #H12 elim (fqu_cpxs_trans_ntdeq … H1 … HTU1 H) -T1 /3 width=8 by fqup_strap2, ex3_intro/ ] qed-. -lemma fqus_cpxs_trans_neq: ∀h,o,G1,G2,L1,L2,T1,T2. ⦃G1, L1, T1⦄ ⊐* ⦃G2, L2, T2⦄ → - ∀U2. ⦃G2, L2⦄ ⊢ T2 ⬈*[h, o] U2 → (T2 = U2 → ⊥) → - ∃∃U1. ⦃G1, L1⦄ ⊢ T1 ⬈*[h, o] U1 & T1 = U1 → ⊥ & ⦃G1, L1, U1⦄ ⊐* ⦃G2, L2, U2⦄. -#h #o #G1 #G2 #L1 #L2 #T1 #T2 #H12 #U2 #HTU2 #H elim (fqus_inv_gen … H12) -H12 -[ #H12 elim (fqup_cpxs_trans_neq … H12 … HTU2 H) -T2 +lemma fqus_cpxs_trans_ntdeq: ∀h,o,b,G1,G2,L1,L2,T1,T2. ⦃G1, L1, T1⦄ ⊐*[b] ⦃G2, L2, T2⦄ → + ∀U2. ⦃G2, L2⦄ ⊢ T2 ⬈*[h] U2 → (T2 ≡[h, o] U2 → ⊥) → + ∃∃U1. ⦃G1, L1⦄ ⊢ T1 ⬈*[h] U1 & T1 ≡[h, o] U1 → ⊥ & ⦃G1, L1, U1⦄ ⊐*[b] ⦃G2, L2, U2⦄. +#h #o #b #G1 #G2 #L1 #L2 #T1 #T2 #H12 #U2 #HTU2 #H elim (fqus_inv_fqup … H12) -H12 +[ #H12 elim (fqup_cpxs_trans_ntdeq … H12 … HTU2 H) -T2 /3 width=4 by fqup_fqus, ex3_intro/ | * #HG #HL #HT destruct /3 width=4 by ex3_intro/ ] diff --git a/matita/matita/contribs/lambdadelta/basic_2/rt_computation/cpxs_lfdeq.ma b/matita/matita/contribs/lambdadelta/basic_2/rt_computation/cpxs_lfdeq.ma new file mode 100644 index 000000000..73119ad53 --- /dev/null +++ b/matita/matita/contribs/lambdadelta/basic_2/rt_computation/cpxs_lfdeq.ma @@ -0,0 +1,49 @@ +(**************************************************************************) +(* ___ *) +(* ||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/cpx_lfdeq.ma". +include "basic_2/rt_computation/cpxs_tdeq.ma". + +(* UNCOUNTED CONTEXT-SENSITIVE PARALLEL RT-COMPUTATION FOR TERMS ************) + +(* Properties with degree-based equivalence for local environments **********) + +(* Basic_2A1: was just: lleq_cpxs_trans *) +lemma lfdeq_cpxs_trans: ∀h,o,G,L0,T0,T1. ⦃G, L0⦄ ⊢ T0 ⬈*[h] T1 → + ∀L2. L2 ≡[h, o, T0] L0 → + ∃∃T. ⦃G, L2⦄ ⊢ T0 ⬈*[h] T & T ≡[h, o] T1. +#h #o #G #L0 #T0 #T1 #H @(cpxs_ind_dx … H) -T0 /2 width=3 by ex2_intro/ +#T0 #T #HT0 #_ #IH #L2 #HL2 +elim (lfdeq_cpx_trans … HL2 … HT0) #U1 #H1 #H2 +elim (IH L2) -IH /2 width=4 by cpx_lfdeq_conf_dx/ -L0 #U2 #H3 #H4 +elim (tdeq_cpxs_trans … H2 … H3) -T #U0 #H2 #H3 +/3 width=5 by cpxs_strap2, tdeq_trans, ex2_intro/ +qed-. + +(* Basic_2A1: was just: cpxs_lleq_conf *) +lemma cpxs_lfdeq_trans: ∀h,o,G,L0,T0,T1. ⦃G, L0⦄ ⊢ T0 ⬈*[h] T1 → + ∀L2. L0 ≡[h, o, T0] L2 → + ∃∃T. ⦃G, L2⦄ ⊢ T0 ⬈*[h] T & T ≡[h, o] T1. +/3 width=3 by lfdeq_cpxs_trans, lfdeq_sym/ qed-. + +(* Basic_2A1: was just: cpxs_lleq_conf_dx *) +lemma cpxs_lfdeq_conf_dx: ∀h,o,G,L2,T1,T2. ⦃G, L2⦄ ⊢ T1 ⬈*[h] T2 → + ∀L1. L1 ≡[h, o, T1] L2 → L1 ≡[h, o, T2] L2. +#h #o #G #L2 #T1 #T2 #H @(cpxs_ind … H) -T2 /3 width=6 by cpx_lfdeq_conf_dx/ +qed-. + +(* Basic_2A1: was just: lleq_conf_sn *) +lemma cpxs_lfdeq_conf_sn: ∀h,o,G,L1,T1,T2. ⦃G, L1⦄ ⊢ T1 ⬈*[h] T2 → + ∀L2. L1 ≡[h, o, T1] L2 → L1 ≡[h, o, T2] L2. +/4 width=6 by cpxs_lfdeq_conf_dx, lfdeq_sym/ qed-. diff --git a/matita/matita/contribs/lambdadelta/basic_2/rt_computation/cpxs_lleq.ma b/matita/matita/contribs/lambdadelta/basic_2/rt_computation/cpxs_lleq.ma deleted file mode 100644 index 2765cf1bc..000000000 --- a/matita/matita/contribs/lambdadelta/basic_2/rt_computation/cpxs_lleq.ma +++ /dev/null @@ -1,39 +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/reduction/cpx_lleq.ma". -include "basic_2/computation/cpxs.ma". - -(* CONTEXT-SENSITIVE EXTENDED PARALLEL COMPUTATION ON TERMS *****************) - -(* Properties on lazy equivalence for local environments ********************) - -lemma lleq_cpxs_trans: ∀h,o,G,L2,T1,T2. ⦃G, L2⦄ ⊢ T1 ⬈*[h, o] T2 → - ∀L1. L1 ≡[T1, 0] L2 → ⦃G, L1⦄ ⊢ T1 ⬈*[h, o] T2. -#h #o #G #L2 #T1 #T2 #H @(cpxs_ind_dx … H) -T1 -/4 width=6 by cpx_lleq_conf_dx, lleq_cpx_trans, cpxs_strap2/ -qed-. - -lemma cpxs_lleq_conf: ∀h,o,G,L2,T1,T2. ⦃G, L2⦄ ⊢ T1 ⬈*[h, o] T2 → - ∀L1. L2 ≡[T1, 0] L1 → ⦃G, L1⦄ ⊢ T1 ⬈*[h, o] T2. -/3 width=3 by lleq_cpxs_trans, lleq_sym/ qed-. - -lemma cpxs_lleq_conf_dx: ∀h,o,G,L2,T1,T2. ⦃G, L2⦄ ⊢ T1 ⬈*[h, o] T2 → - ∀L1. L1 ≡[T1, 0] L2 → L1 ≡[T2, 0] L2. -#h #o #G #L2 #T1 #T2 #H @(cpxs_ind … H) -T2 /3 width=6 by cpx_lleq_conf_dx/ -qed-. - -lemma cpxs_lleq_conf_sn: ∀h,o,G,L1,T1,T2. ⦃G, L1⦄ ⊢ T1 ⬈*[h, o] T2 → - ∀L2. L1 ≡[T1, 0] L2 → L1 ≡[T2, 0] L2. -/4 width=6 by cpxs_lleq_conf_dx, lleq_sym/ 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 561a9980b..2123e5fd9 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 @@ -119,7 +119,7 @@ table { [ "csx ( ⦃?,?⦄ ⊢ ⬈*[?,?] 𝐒⦃?⦄ )" "csx_simple" + "csx_simple_theq" + "csx_drops" + "csx_lsubr" + "csx_aaa" + "csx_gcp" + "csx_gcr" + "csx_lfpx" + "csx_cnx" + "csx_cpxs" + "csx_csx" * ] *) [ "lfpxs ( ⦃?,?⦄ ⊢ ⬈*[?,?] ? )" "lfpxs_length" + "lfpxs_drops" + "lfpxs_fqup" + "lfpxs_lfdeq" + "lfpxs_aaa" + "lfpxs_cpxs" + "lfpxs_lfpxs" * ] - [ "cpxs ( ⦃?,?⦄ ⊢ ? ⬈*[?] ? )" "cpxs_tdeq" + "cpxs_theq" + "cpxs_theq_vector" + "cpxs_drops" + "cpxs_lsubr" + "cpxs_aaa" + "cpxs_lfpx" + "cpxs_cnx" + "cpxs_cpxs" * ] + [ "cpxs ( ⦃?,?⦄ ⊢ ? ⬈*[?] ? )" "cpxs_tdeq" + "cpxs_theq" + "cpxs_theq_vector" + "cpxs_drops" + "cpxs_fqus" + "cpxs_lsubr" + "cpxs_lfdeq" + "cpxs_aaa" + "cpxs_lfpx" + "cpxs_cnx" + "cpxs_cpxs" * ] } ] }