X-Git-Url: http://matita.cs.unibo.it/gitweb/?a=blobdiff_plain;ds=inline;f=matita%2Fmatita%2Fcontribs%2Flambdadelta%2Fbasic_2%2Fcomputation%2Fcpxs_lift.ma;h=182043d3b5d4f704d8d254aeccbc9604cb4b9eac;hb=82fe07c3accb68ca4f7a1870a046128fe980dced;hp=9e93e1d29a97be59204dc2a841d5f229ef47e8ef;hpb=82500a9ceb53e1af0263c22afbd5954fa3a83190;p=helm.git diff --git a/matita/matita/contribs/lambdadelta/basic_2/computation/cpxs_lift.ma b/matita/matita/contribs/lambdadelta/basic_2/computation/cpxs_lift.ma index 9e93e1d29..182043d3b 100644 --- a/matita/matita/contribs/lambdadelta/basic_2/computation/cpxs_lift.ma +++ b/matita/matita/contribs/lambdadelta/basic_2/computation/cpxs_lift.ma @@ -13,6 +13,7 @@ (**************************************************************************) include "basic_2/substitution/fsups_fsups.ma". +include "basic_2/unfold/lsstas_lift.ma". include "basic_2/reduction/cpx_lift.ma". include "basic_2/computation/cpxs.ma". @@ -20,13 +21,25 @@ include "basic_2/computation/cpxs.ma". (* Advanced properties ******************************************************) +lemma lsstas_cpxs: ∀h,g,G,L,T1,T2,l1. ⦃G, L⦄ ⊢ T1 •* [h, g, l1] T2 → + ∀l2. ⦃G, L⦄ ⊢ T1 ▪ [h, g] l2 → l1 ≤ l2 → ⦃G, L⦄ ⊢ T1 ➡*[h, g] T2. +#h #g #G #L #T1 #T2 #l1 #H @(lsstas_ind_dx … H) -T2 -l1 // +#l1 #T #T2 #HT1 #HT2 #IHT1 #l2 #Hl2 #Hl12 +lapply (lsstas_da_conf … HT1 … Hl2) -HT1 +>(plus_minus_m_m (l2-l1) 1 ?) +[ /4 width=5 by cpxs_strap1, ssta_cpx, lt_to_le/ +| /2 width=1 by monotonic_le_minus_r/ +] +qed. + lemma cpxs_delta: ∀h,g,I,G,L,K,V,V2,i. ⇩[0, i] L ≡ K.ⓑ{I}V → ⦃G, K⦄ ⊢ V ➡*[h, g] V2 → ∀W2. ⇧[0, i + 1] V2 ≡ W2 → ⦃G, L⦄ ⊢ #i ➡*[h, g] W2. -#h #g #I #G #L #K #V #V2 #i #HLK #H elim H -V2 [ /3 width=9/ ] -#V1 #V2 #_ #HV12 #IHV1 #W2 #HVW2 -lapply (ldrop_fwd_ldrop2 … HLK) -HLK #HLK -elim (lift_total V1 0 (i+1)) /4 width=11 by cpx_lift, cpxs_strap1/ +#h #g #I #G #L #K #V #V2 #i #HLK #H elim H -V2 +[ /3 width=9 by cpx_cpxs, cpx_delta/ +| #V1 lapply (ldrop_fwd_ldrop2 … HLK) -HLK + elim (lift_total V1 0 (i+1)) /4 width=11 by cpx_lift, cpxs_strap1/ +] qed. (* Advanced inversion lemmas ************************************************) @@ -35,21 +48,22 @@ lemma cpxs_inv_lref1: ∀h,g,G,L,T2,i. ⦃G, L⦄ ⊢ #i ➡*[h, g] T2 → T2 = #i ∨ ∃∃I,K,V1,T1. ⇩[0, i] L ≡ K.ⓑ{I}V1 & ⦃G, K⦄ ⊢ V1 ➡*[h, g] T1 & ⇧[0, i + 1] T1 ≡ T2. -#h #g #G #L #T2 #i #H @(cpxs_ind … H) -T2 /2 width=1/ +#h #g #G #L #T2 #i #H @(cpxs_ind … H) -T2 /2 width=1 by or_introl/ #T #T2 #_ #HT2 * [ #H destruct - elim (cpx_inv_lref1 … HT2) -HT2 /2 width=1/ - * /4 width=7/ + elim (cpx_inv_lref1 … HT2) -HT2 /2 width=1 by or_introl/ + * /4 width=7 by cpx_cpxs, ex3_4_intro, or_intror/ | * #I #K #V1 #T1 #HLK #HVT1 #HT1 lapply (ldrop_fwd_ldrop2 … HLK) #H0LK - elim (cpx_inv_lift1 … HT2 … H0LK … HT1) -H0LK -T /4 width=7/ + elim (cpx_inv_lift1 … HT2 … H0LK … HT1) -H0LK -T + /4 width=7 by cpxs_strap1, ex3_4_intro, or_intror/ ] qed-. (* Relocation properties ****************************************************) lemma cpxs_lift: ∀h,g,G. l_liftable (cpxs h g G). -/3 width=9/ qed. +/3 width=9 by cpx_lift, cpxs_strap1, l_liftable_LTC/ qed. lemma cpxs_inv_lift1: ∀h,g,G. l_deliftable_sn (cpxs h g G). /3 width=5 by l_deliftable_sn_LTC, cpx_inv_lift1/ @@ -60,23 +74,44 @@ qed-. lemma fsupq_cpxs_trans: ∀h,g,G1,G2,L1,L2,T2,U2. ⦃G2, L2⦄ ⊢ T2 ➡*[h, g] U2 → ∀T1. ⦃G1, L1, T1⦄ ⊃⸮ ⦃G2, L2, T2⦄ → ∃∃U1. ⦃G1, L1⦄ ⊢ T1 ➡*[h, g] U1 & ⦃G1, L1, U1⦄ ⊃* ⦃G2, L2, U2⦄. -#h #g #G1 #G2 #L1 #L2 #T2 #U2 #H @(cpxs_ind_dx … H) -T2 [ /3 width=3/ ] -#T #T2 #HT2 #_ #IHTU2 #T1 #HT1 -elim (fsupq_cpx_trans … HT1 … HT2) -T #T #HT1 #HT2 -elim (IHTU2 … HT2) -T2 /3 width=3/ +#h #g #G1 #G2 #L1 #L2 #T2 #U2 #H @(cpxs_ind_dx … H) -T2 +[ /3 width=3 by fsupq_fsups, ex2_intro/ +| #T #T2 #HT2 #_ #IHTU2 #T1 #HT1 + elim (fsupq_cpx_trans … HT1 … HT2) -T #T #HT1 #HT2 + elim (IHTU2 … HT2) -T2 /3 width=3 by cpxs_strap2, ex2_intro/ +] qed-. +lemma fsupq_lsstas_trans: ∀h,g,G1,G2,L1,L2,T1,T2. ⦃G1, L1, T1⦄ ⊃⸮ ⦃G2, L2, T2⦄ → + ∀U2,l1. ⦃G2, L2⦄ ⊢ T2 •*[h, g, l1] U2 → + ∀l2. ⦃G2, L2⦄ ⊢ T2 ▪ [h, g] l2 → l1 ≤ l2 → + ∃∃U1. ⦃G1, L1⦄ ⊢ T1 ➡*[h, g] U1 & ⦃G1, L1, U1⦄ ⊃* ⦃G2, L2, U2⦄. +/3 width=5 by fsupq_cpxs_trans, lsstas_cpxs/ qed-. + lemma fsups_cpxs_trans: ∀h,g,G1,G2,L1,L2,T1,T2. ⦃G1, L1, T1⦄ ⊃* ⦃G2, L2, T2⦄ → ∀U2. ⦃G2, L2⦄ ⊢ T2 ➡*[h, g] U2 → ∃∃U1. ⦃G1, L1⦄ ⊢ T1 ➡*[h, g] U1 & ⦃G1, L1, U1⦄ ⊃* ⦃G2, L2, U2⦄. -#h #g #G1 #G2 #L1 #L2 #T1 #T2 #H @(fsups_ind … H) -G2 -L2 -T2 [ /2 width=3/ ] -#G #G2 #L #L2 #T #T2 #_ #HT2 #IHT1 #U2 #HTU2 -elim (fsupq_cpxs_trans … HTU2 … HT2) -T2 #T2 #HT2 #HTU2 -elim (IHT1 … HT2) -T #T #HT1 #HT2 -lapply (fsups_trans … HT2 … HTU2) -G -L -T2 /2 width=3/ +#h #g #G1 #G2 #L1 #L2 #T1 #T2 #H @(fsups_ind … H) -G2 -L2 -T2 +[ /2 width=3 by ex2_intro/ +| #G #G2 #L #L2 #T #T2 #_ #HT2 #IHT1 #U2 #HTU2 + elim (fsupq_cpxs_trans … HTU2 … HT2) -T2 #T2 #HT2 #HTU2 + elim (IHT1 … HT2) -T /3 width=7 by fsups_trans, ex2_intro/ +] qed-. -lemma fsup_ssta_trans: ∀h,g,G1,G2,L1,L2,T1,T2. ⦃G1, L1, T1⦄ ⊃ ⦃G2, L2, T2⦄ → - ∀U2,l. ⦃G2, L2⦄ ⊢ T2 •[h, g] ⦃l+1, U2⦄ → - ∃∃U1. ⦃G1, L1⦄ ⊢ T1 ➡[h, g] U1 & ⦃G1, L1, U1⦄ ⊃⸮ ⦃G2, L2, U2⦄. -/3 width=4 by fsup_cpx_trans, ssta_cpx/ qed-. +lemma fsups_lsstas_trans: ∀h,g,G1,G2,L1,L2,T1,T2. ⦃G1, L1, T1⦄ ⊃* ⦃G2, L2, T2⦄ → + ∀U2,l1. ⦃G2, L2⦄ ⊢ T2 •*[h, g, l1] U2 → + ∀l2. ⦃G2, L2⦄ ⊢ T2 ▪ [h, g] l2 → l1 ≤ l2 → + ∃∃U1. ⦃G1, L1⦄ ⊢ T1 ➡*[h, g] U1 & ⦃G1, L1, U1⦄ ⊃* ⦃G2, L2, U2⦄. +/3 width=7 by fsups_cpxs_trans, lsstas_cpxs/ qed-. + +lemma fsups_cpx_trans: ∀h,g,G1,G2,L1,L2,T1,T2. ⦃G1, L1, T1⦄ ⊃* ⦃G2, L2, T2⦄ → + ∀U2. ⦃G2, L2⦄ ⊢ T2 ➡[h, g] U2 → + ∃∃U1. ⦃G1, L1⦄ ⊢ T1 ➡[h, g] U1 & ⦃G1, L1, U1⦄ ⊃* ⦃G2, L2, U2⦄. +#h #g #G1 #G2 #L1 #L2 #T1 #T2 #H @(fsups_ind … H) -G2 -L2 -T2 +[ /2 width=3 by ex2_intro/ +| #G #G2 #L #L2 #T #T2 #_ #HT2 #IHT1 #U2 #HTU2 + elim (fsupq_cpx_trans … HT2 … HTU2) -T2 #T2 #HT2 #HTU2 + elim (IHT1 … HT2) -T /3 width=7 by fsups_strap1, ex2_intro/ +] +qed-. \ No newline at end of file