X-Git-Url: http://matita.cs.unibo.it/gitweb/?a=blobdiff_plain;f=matita%2Fmatita%2Fcontribs%2Flambdadelta%2Fbasic_2%2Frt_computation%2Fcpxs_rdeq.ma;fp=matita%2Fmatita%2Fcontribs%2Flambdadelta%2Fbasic_2%2Frt_computation%2Fcpxs_rdeq.ma;h=292dc54e1609be9441ec59872869e10e29865fba;hb=222044da28742b24584549ba86b1805a87def070;hp=0000000000000000000000000000000000000000;hpb=5c186c72f508da0849058afeecc6877cd9ed6303;p=helm.git diff --git a/matita/matita/contribs/lambdadelta/basic_2/rt_computation/cpxs_rdeq.ma b/matita/matita/contribs/lambdadelta/basic_2/rt_computation/cpxs_rdeq.ma new file mode 100644 index 000000000..292dc54e1 --- /dev/null +++ b/matita/matita/contribs/lambdadelta/basic_2/rt_computation/cpxs_rdeq.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_rdeq.ma". +include "basic_2/rt_computation/cpxs_tdeq.ma". + +(* UNBOUND CONTEXT-SENSITIVE PARALLEL RT-COMPUTATION FOR TERMS **************) + +(* Properties with degree-based equivalence for local environments **********) + +(* Basic_2A1: was just: lleq_cpxs_trans *) +lemma rdeq_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 (rdeq_cpx_trans … HL2 … HT0) #U1 #H1 #H2 +elim (IH L2) -IH /2 width=4 by cpx_rdeq_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_rdeq_conf: ∀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 rdeq_cpxs_trans, rdeq_sym/ qed-. + +(* Basic_2A1: was just: cpxs_lleq_conf_dx *) +lemma cpxs_rdeq_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_rdeq_conf_dx/ +qed-. + +(* Basic_2A1: was just: lleq_conf_sn *) +lemma cpxs_rdeq_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_rdeq_conf_dx, rdeq_sym/ qed-.