X-Git-Url: http://matita.cs.unibo.it/gitweb/?a=blobdiff_plain;f=matita%2Fmatita%2Fcontribs%2Flambdadelta%2Fbasic_2%2Fdynamic%2Fygt.ma;h=43cc6d0551896bcc8b19a3b6e3a74e0a0ce74603;hb=4eebf1cf684c8a7946b71174ee6145673af49309;hp=7b50bfdcfd08da392bfebb3c24325068815fa8d6;hpb=29973426e0227ee48368d1c24dc0c17bf2baef77;p=helm.git diff --git a/matita/matita/contribs/lambdadelta/basic_2/dynamic/ygt.ma b/matita/matita/contribs/lambdadelta/basic_2/dynamic/ygt.ma index 7b50bfdcf..43cc6d055 100644 --- a/matita/matita/contribs/lambdadelta/basic_2/dynamic/ygt.ma +++ b/matita/matita/contribs/lambdadelta/basic_2/dynamic/ygt.ma @@ -12,67 +12,67 @@ (* *) (**************************************************************************) -include "basic_2/notation/relations/btpredstarproper_6.ma". +include "basic_2/notation/relations/btpredstarproper_8.ma". include "basic_2/dynamic/ysc.ma". include "basic_2/dynamic/yprs.ma". (* "BIG TREE" PROPER PARALLEL COMPUTATION FOR CLOSURES **********************) -inductive ygt (h) (g) (L1) (T1): relation2 lenv term ≝ -| ygt_inj : ∀L,L2,T,T2. h ⊢ ⦃L1, T1⦄ ≥[h, g] ⦃L, T⦄ → h ⊢ ⦃L, T⦄ ≻[h, g] ⦃L2, T2⦄ → - ygt h g L1 T1 L2 T2 -| ygt_step: ∀L,L2,T. ygt h g L1 T1 L T → ⦃G, L⦄ ⊢ ➡ L2 → ygt h g L1 T1 L2 T +inductive ygt (h) (g) (G1) (L1) (T1): relation3 genv lenv term ≝ +| ygt_inj : ∀G,G2,L,L2,T,T2. ⦃G1, L1, T1⦄ ≥[h, g] ⦃G, L, T⦄ → ⦃G, L, T⦄ ≻[h, g] ⦃G2, L2, T2⦄ → + ygt h g G1 L1 T1 G2 L2 T2 +| ygt_step: ∀G,L,L2,T. ygt h g G1 L1 T1 G L T → ⦃G, L⦄ ⊢ ➡ L2 → ygt h g G1 L1 T1 G L2 T . interpretation "'big tree' proper parallel computation (closure)" - 'BTPRedStarProper h g L1 T1 L2 T2 = (ygt h g L1 T1 L2 T2). + 'BTPRedStarProper h g G1 L1 T1 G2 L2 T2 = (ygt h g G1 L1 T1 G2 L2 T2). (* Basic forvard lemmas *****************************************************) -lemma ygt_fwd_yprs: ∀h,g,L1,L2,T1,T2. h ⊢ ⦃L1, T1⦄ >[h, g] ⦃L2, T2⦄ → - h ⊢ ⦃L1, T1⦄ ≥[h, g] ⦃L2, T2⦄. -#h #g #L1 #L2 #T1 #T2 #H elim H -L2 -T2 -/3 width=4 by yprs_strap1, ysc_ypr, ypr_lpr/ +lemma ygt_fwd_yprs: ∀h,g,G1,G2,L1,L2,T1,T2. ⦃G1, L1, T1⦄ >[h, g] ⦃G2, L2, T2⦄ → + ⦃G1, L1, T1⦄ ≥[h, g] ⦃G2, L2, T2⦄. +#h #g #G1 #G2 #L1 #L2 #T1 #T2 #H elim H -G2 -L2 -T2 +/3 width=5 by yprs_strap1, ysc_ypr, ypr_lpr/ qed-. (* Basic properties *********************************************************) -lemma ysc_ygt: ∀h,g,L1,L2,T1,T2. h ⊢ ⦃L1, T1⦄ ≻[h, g] ⦃L2, T2⦄ → - h ⊢ ⦃L1, T1⦄ >[h, g] ⦃L2, T2⦄. -/3 width=4/ qed. +lemma ysc_ygt: ∀h,g,G1,G2,L1,L2,T1,T2. ⦃G1, L1, T1⦄ ≻[h, g] ⦃G2, L2, T2⦄ → + ⦃G1, L1, T1⦄ >[h, g] ⦃G2, L2, T2⦄. +/3 width=5/ qed. -lemma ygt_strap1: ∀h,g,L1,L,L2,T1,T,T2. h ⊢ ⦃L1, T1⦄ >[h, g] ⦃L, T⦄ → - h ⊢ ⦃L, T⦄ ≽[h, g] ⦃L2, T2⦄ → h ⊢ ⦃L1, T1⦄ >[h, g] ⦃L2, T2⦄. -#h #g #L1 #L #L2 #T1 #T #T2 #H1 #H2 +lemma ygt_strap1: ∀h,g,G1,G,G2,L1,L,L2,T1,T,T2. ⦃G1, L1, T1⦄ >[h, g] ⦃G, L, T⦄ → + ⦃G, L, T⦄ ≽[h, g] ⦃G2, L2, T2⦄ → ⦃G1, L1, T1⦄ >[h, g] ⦃G2, L2, T2⦄. +#h #g #G1 #G #G2 #L1 #L #L2 #T1 #T #T2 #H1 #H2 lapply (ygt_fwd_yprs … H1) #H0 -elim (ypr_inv_ysc … H2) -H2 [| * #HL2 #H destruct ] /2 width=4/ +elim (ypr_inv_ysc … H2) -H2 [| * #HG2 #HL2 #HT2 destruct ] /2 width=5/ qed-. -lemma ygt_strap2: ∀h,g,L1,L,L2,T1,T,T2. h ⊢ ⦃L1, T1⦄ ≽[h, g] ⦃L, T⦄ → - h ⊢ ⦃L, T⦄ >[h, g] ⦃L2, T2⦄ → h ⊢ ⦃L1, T1⦄ >[h, g] ⦃L2, T2⦄. -#h #g #L1 #L #L2 #T1 #T #T2 #H1 #H2 elim H2 -L2 -T2 -[ /3 width=4 by ygt_inj, yprs_strap2/ | /2 width=3/ ] +lemma ygt_strap2: ∀h,g,G1,G,G2,L1,L,L2,T1,T,T2. ⦃G1, L1, T1⦄ ≽[h, g] ⦃G, L, T⦄ → + ⦃G, L, T⦄ >[h, g] ⦃G2, L2, T2⦄ → ⦃G1, L1, T1⦄ >[h, g] ⦃G2, L2, T2⦄. +#h #g #G1 #G #G2 #L1 #L #L2 #T1 #T #T2 #H1 #H2 elim H2 -G2 -L2 -T2 +[ /3 width=5 by ygt_inj, yprs_strap2/ | /2 width=3/ ] qed-. -lemma ygt_yprs_trans: ∀h,g,L1,L,L2,T1,T,T2. h ⊢ ⦃L1, T1⦄ >[h, g] ⦃L, T⦄ → - h ⊢ ⦃L, T⦄ ≥[h, g] ⦃L2, T2⦄ → h ⊢ ⦃L1, T1⦄ >[h, g] ⦃L2, T2⦄. -#h #g #L1 #L #L2 #T1 #T #T2 #HT1 #HT2 @(yprs_ind … HT2) -L2 -T2 // -/2 width=4 by ygt_strap1/ +lemma ygt_yprs_trans: ∀h,g,G1,G,G2,L1,L,L2,T1,T,T2. ⦃G1, L1, T1⦄ >[h, g] ⦃G, L, T⦄ → + ⦃G, L, T⦄ ≥[h, g] ⦃G2, L2, T2⦄ → ⦃G1, L1, T1⦄ >[h, g] ⦃G2, L2, T2⦄. +#h #g #G1 #G #G2 #L1 #L #L2 #T1 #T #T2 #HT1 #HT2 @(yprs_ind … HT2) -G2 -L2 -T2 // +/2 width=5 by ygt_strap1/ qed-. -lemma yprs_ygt_trans: ∀h,g,L1,L,T1,T. h ⊢ ⦃L1, T1⦄ ≥[h, g] ⦃L, T⦄ → - ∀L2,T2. h ⊢ ⦃L, T⦄ >[h, g] ⦃L2, T2⦄ → h ⊢ ⦃L1, T1⦄ >[h, g] ⦃L2, T2⦄. -#h #g #L1 #L #T1 #T #HT1 @(yprs_ind … HT1) -L -T // -/3 width=4 by ygt_strap2/ +lemma yprs_ygt_trans: ∀h,g,G1,G,L1,L,T1,T. ⦃G1, L1, T1⦄ ≥[h, g] ⦃G, L, T⦄ → + ∀G2,L2,T2. ⦃G, L, T⦄ >[h, g] ⦃G2, L2, T2⦄ → ⦃G1, L1, T1⦄ >[h, g] ⦃G2, L2, T2⦄. +#h #g #G1 #G #L1 #L #T1 #T #HT1 @(yprs_ind … HT1) -G -L -T // +/3 width=5 by ygt_strap2/ qed-. -lemma fsupp_ygt: ∀h,g,L1,L2,T1,T2. ⦃L1, T1⦄ ⊃+ ⦃L2, T2⦄ → h ⊢ ⦃L1, T1⦄ >[h, g] ⦃L2, T2⦄. -#h #g #L1 #L2 #T1 #T2 #H @(fsupp_ind … L2 T2 H) -L2 -T2 /3 width=1/ /3 width=4/ +lemma fsupp_ygt: ∀h,g,G1,G2,L1,L2,T1,T2. ⦃G1, L1, T1⦄ ⊃+ ⦃G2, L2, T2⦄ → ⦃G1, L1, T1⦄ >[h, g] ⦃G2, L2, T2⦄. +#h #g #G1 #G2 #L1 #L2 #T1 #T2 #H @(fsupp_ind … L2 T2 H) -G2 -L2 -T2 /3 width=1/ /3 width=5/ qed. -lemma cprs_ygt: ∀h,g,L,T1,T2. ⦃G, L⦄ ⊢ T1 ➡* T2 → (T1 = T2 → ⊥) → - h ⊢ ⦃L, T1⦄ >[h, g] ⦃L, T2⦄. -#h #g #L #T1 #T2 #H @(cprs_ind … H) -T2 +lemma cprs_ygt: ∀h,g,G,L,T1,T2. ⦃G, L⦄ ⊢ T1 ➡* T2 → (T1 = T2 → ⊥) → + ⦃G, L, T1⦄ >[h, g] ⦃G, L, T2⦄. +#h #g #G #L #T1 #T2 #H @(cprs_ind … H) -T2 [ #H elim H // | #T #T2 #_ #HT2 #IHT1 #HT12 elim (term_eq_dec T1 T) #H destruct @@ -83,19 +83,6 @@ lemma cprs_ygt: ∀h,g,L,T1,T2. ⦃G, L⦄ ⊢ T1 ➡* T2 → (T1 = T2 → ⊥) ] qed. -lemma sstas_ygt: ∀h,g,L,T1,T2. ⦃G, L⦄ ⊢ T1 •*[h, g] T2 → (T1 = T2 → ⊥) → - h ⊢ ⦃L, T1⦄ >[h, g] ⦃L, T2⦄. -#h #g #L #T1 #T2 #H @(sstas_ind … H) -T2 -[ #H elim H // -| #T #T2 #l #_ #HT2 #IHT1 #HT12 -HT12 - elim (term_eq_dec T1 T) #H destruct - [ -IHT1 /3 width=2/ - | lapply (IHT1 … H) -IHT1 -H #HT1 - @(ygt_strap1 … HT1) -HT1 /2 width=2/ - ] -] -qed. - -lemma lsubsv_ygt: ∀h,g,L1,L2,T. h ⊢ L2 ¡⊑[h, g] L1 → (L1 = L2 → ⊥) → - h ⊢ ⦃L1, T⦄ >[h, g] ⦃L2, T⦄. +lemma lsubsv_ygt: ∀h,g,G,L1,L2,T. G ⊢ L2 ¡⊑[h, g] L1 → (L1 = L2 → ⊥) → + ⦃G, L1, T⦄ >[h, g] ⦃G, L2, T⦄. /4 width=1/ qed.