X-Git-Url: http://matita.cs.unibo.it/gitweb/?a=blobdiff_plain;f=matita%2Fmatita%2Fcontribs%2Flambdadelta%2Fbasic_2%2Fcomputation%2Fcpds.ma;h=a2eb234833db6cbc8d83b8ce0c5b27d4e0ca721a;hb=c2211ba58807254e75c6321cbd688db462d80fd2;hp=bf329f7379c730d3f7016b821b890a713c1678f5;hpb=d8ddeb030acbf2246693dc0b65c321ee39e4328b;p=helm.git diff --git a/matita/matita/contribs/lambdadelta/basic_2/computation/cpds.ma b/matita/matita/contribs/lambdadelta/basic_2/computation/cpds.ma index bf329f737..a2eb23483 100644 --- a/matita/matita/contribs/lambdadelta/basic_2/computation/cpds.ma +++ b/matita/matita/contribs/lambdadelta/basic_2/computation/cpds.ma @@ -12,36 +12,47 @@ (* *) (**************************************************************************) -include "basic_2/notation/relations/dpredstar_6.ma". +include "basic_2/notation/relations/dpredstar_7.ma". include "basic_2/static/da.ma". include "basic_2/unfold/lstas.ma". include "basic_2/computation/cprs.ma". (* DECOMPOSED EXTENDED PARALLEL COMPUTATION ON TERMS ************************) -definition cpds: ∀h. sd h → relation4 genv lenv term term ≝ - λh,g,G,L,T1,T2. - ∃∃T,l1,l2. l2 ≤ l1 & ⦃G, L⦄ ⊢ T1 ▪[h, g] l1 & ⦃G, L⦄ ⊢ T1 •*[h, l2] T & ⦃G, L⦄ ⊢ T ➡* T2. +definition cpds: ∀h. sd h → nat → relation4 genv lenv term term ≝ + λh,g,l2,G,L,T1,T2. + ∃∃T,l1. l2 ≤ l1 & ⦃G, L⦄ ⊢ T1 ▪[h, g] l1 & ⦃G, L⦄ ⊢ T1 •*[h, l2] T & ⦃G, L⦄ ⊢ T ➡* T2. interpretation "decomposed extended parallel computation (term)" - 'DPRedStar h g G L T1 T2 = (cpds h g G L T1 T2). + 'DPRedStar h g l G L T1 T2 = (cpds h g l G L T1 T2). (* Basic properties *********************************************************) lemma sta_cprs_cpds: ∀h,g,G,L,T1,T,T2,l. ⦃G, L⦄ ⊢ T1 ▪[h, g] l+1 → ⦃G, L⦄ ⊢ T1 •[h] T → - ⦃G, L⦄ ⊢ T ➡* T2 → ⦃G, L⦄ ⊢ T1 •*➡*[h, g] T2. -/3 width=7 by sta_lstas, ex4_3_intro/ qed. + ⦃G, L⦄ ⊢ T ➡* T2 → ⦃G, L⦄ ⊢ T1 •*➡*[h, g, 1] T2. +/3 width=6 by sta_lstas, ex4_2_intro/ qed. -lemma lstas_cpds: ∀h,g,G,L,T1,T2,l. ⦃G, L⦄ ⊢ T1 ▪[h, g] l → ⦃G, L⦄ ⊢ T1 •*[h, l] T2 → ⦃G, L⦄ ⊢ T1 •*➡*[h, g] T2. -/2 width=7 by ex4_3_intro/ qed. +lemma lstas_cpds: ∀h,g,G,L,T1,T2,l1. ⦃G, L⦄ ⊢ T1 ▪[h, g] l1 → + ∀l2. l2 ≤ l1 → ⦃G, L⦄ ⊢ T1 •*[h, l2] T2 → ⦃G, L⦄ ⊢ T1 •*➡*[h, g, l2] T2. +/2 width=6 by ex4_2_intro/ qed. -lemma cprs_cpds: ∀h,g,G,L,T1,T2,l. ⦃G, L⦄ ⊢ T1 ▪[h, g] l → ⦃G, L⦄ ⊢ T1 ➡* T2 → ⦃G, L⦄ ⊢ T1 •*➡*[h, g] T2. -/2 width=7 by lstar_O, ex4_3_intro/ qed. +lemma cprs_cpds: ∀h,g,G,L,T1,T2,l. ⦃G, L⦄ ⊢ T1 ▪[h, g] l → ⦃G, L⦄ ⊢ T1 ➡* T2 → + ⦃G, L⦄ ⊢ T1 •*➡*[h, g, 0] T2. +/2 width=6 by lstar_O, ex4_2_intro/ qed. -lemma cpds_refl: ∀h,g,G,L,T,l. ⦃G, L⦄ ⊢ T ▪[h, g] l → ⦃G, L⦄ ⊢ T •*➡*[h, g] T. +lemma cpds_refl: ∀h,g,G,L,T,l. ⦃G, L⦄ ⊢ T ▪[h, g] l → ⦃G, L⦄ ⊢ T •*➡*[h, g, 0] T. /2 width=2 by cprs_cpds/ qed. -lemma cpds_strap1: ∀h,g,G,L,T1,T,T2. - ⦃G, L⦄ ⊢ T1 •*➡*[h, g] T → ⦃G, L⦄ ⊢ T ➡ T2 → ⦃G, L⦄ ⊢ T1 •*➡*[h, g] T2. -#h #g #G #L #T1 #T #T2 * /3 width=9 by cprs_strap1, ex4_3_intro/ +lemma cpds_strap1: ∀h,g,G,L,T1,T,T2,l. + ⦃G, L⦄ ⊢ T1 •*➡*[h, g, l] T → ⦃G, L⦄ ⊢ T ➡ T2 → ⦃G, L⦄ ⊢ T1 •*➡*[h, g, l] T2. +#h #g #G #L #T1 #T #T2 #l * /3 width=8 by cprs_strap1, ex4_2_intro/ qed. + +(* Basic forward lemmas *****************************************************) + +lemma cpds_fwd_cprs: ∀h,g,G,L,T1,T2. ⦃G, L⦄ ⊢ T1 •*➡*[h, g, 0] T2 → + ⦃G, L⦄ ⊢ T1 ➡* T2. +#h #g #G #L #T1 #T2 * +#T #l #_ #_ #H lapply (lstas_inv_O … H) -l -H +#H destruct // +qed-.