X-Git-Url: http://matita.cs.unibo.it/gitweb/?p=helm.git;a=blobdiff_plain;f=matita%2Fmatita%2Fcontribs%2Flambdadelta%2Fbasic_2%2Frt_computation%2Flpxs_cpxs.ma;h=71742516cce320c28e7e12cc6cad368299672ee6;hp=6e1a9e2153316624928f75d7abcf7010a2377ef6;hb=19a25bf176255055193372554437729a6fa1894c;hpb=e9da8e091898b6e67a2f270581bdc5cdbe80e9b0 diff --git a/matita/matita/contribs/lambdadelta/basic_2/rt_computation/lpxs_cpxs.ma b/matita/matita/contribs/lambdadelta/basic_2/rt_computation/lpxs_cpxs.ma index 6e1a9e215..71742516c 100644 --- a/matita/matita/contribs/lambdadelta/basic_2/rt_computation/lpxs_cpxs.ma +++ b/matita/matita/contribs/lambdadelta/basic_2/rt_computation/lpxs_cpxs.ma @@ -12,150 +12,50 @@ (* *) (**************************************************************************) -include "basic_2/computation/cpxs_cpxs.ma". -include "basic_2/computation/lpxs.ma". +include "basic_2/rt_computation/lpxs_lpx.ma". -(* SN EXTENDED PARALLEL COMPUTATION ON LOCAL ENVIRONMENTS *******************) +(* UNBOUND PARALLEL RT-COMPUTATION FOR FULL LOCAL ENVIRONMENTS **************) -(* Advanced properties ******************************************************) +(* Properties with context-sensitive extended rt-computation for terms ******) -lemma lpxs_pair: ∀h,o,I,G,L1,L2. ⦃G, L1⦄ ⊢ ➡*[h, o] L2 → - ∀V1,V2. ⦃G, L1⦄ ⊢ V1 ➡*[h, o] V2 → - ⦃G, L1.ⓑ{I}V1⦄ ⊢ ➡*[h, o] L2.ⓑ{I}V2. -/2 width=1 by TC_lpx_sn_pair/ qed. - -(* Advanced inversion lemmas ************************************************) - -lemma lpxs_inv_pair1: ∀h,o,I,G,K1,L2,V1. ⦃G, K1.ⓑ{I}V1⦄ ⊢ ➡*[h, o] L2 → - ∃∃K2,V2. ⦃G, K1⦄ ⊢ ➡*[h, o] K2 & ⦃G, K1⦄ ⊢ V1 ➡*[h, o] V2 & L2 = K2.ⓑ{I}V2. -/3 width=3 by TC_lpx_sn_inv_pair1, lpx_cpxs_trans/ qed-. - -lemma lpxs_inv_pair2: ∀h,o,I,G,L1,K2,V2. ⦃G, L1⦄ ⊢ ➡*[h, o] K2.ⓑ{I}V2 → - ∃∃K1,V1. ⦃G, K1⦄ ⊢ ➡*[h, o] K2 & ⦃G, K1⦄ ⊢ V1 ➡*[h, o] V2 & L1 = K1.ⓑ{I}V1. -/3 width=3 by TC_lpx_sn_inv_pair2, lpx_cpxs_trans/ qed-. - -(* Advanced eliminators *****************************************************) - -lemma lpxs_ind_alt: ∀h,o,G. ∀R:relation lenv. - R (⋆) (⋆) → ( - ∀I,K1,K2,V1,V2. - ⦃G, K1⦄ ⊢ ➡*[h, o] K2 → ⦃G, K1⦄ ⊢ V1 ➡*[h, o] V2 → - R K1 K2 → R (K1.ⓑ{I}V1) (K2.ⓑ{I}V2) - ) → - ∀L1,L2. ⦃G, L1⦄ ⊢ ➡*[h, o] L2 → R L1 L2. -/3 width=4 by TC_lpx_sn_ind, lpx_cpxs_trans/ qed-. - -(* Properties on context-sensitive extended parallel computation for terms **) - -lemma lpxs_cpx_trans: ∀h,o,G. b_c_transitive … (cpx h o G) (λ_.lpxs h o G). -/3 width=5 by b_c_trans_LTC2, lpx_cpxs_trans/ qed-. - -(* Note: alternative proof: /3 width=5 by s_r_trans_TC1, lpxs_cpx_trans/ *) -lemma lpxs_cpxs_trans: ∀h,o,G. b_rs_transitive … (cpx h o G) (λ_.lpxs h o G). -#h #o #G @b_c_to_b_rs_trans @b_c_trans_LTC2 -@b_rs_trans_TC1 /2 width=3 by lpx_cpxs_trans/ (**) (* full auto too slow *) -qed-. - -lemma cpxs_bind2: ∀h,o,G,L,V1,V2. ⦃G, L⦄ ⊢ V1 ➡*[h, o] V2 → - ∀I,T1,T2. ⦃G, L.ⓑ{I}V2⦄ ⊢ T1 ➡*[h, o] T2 → - ∀a. ⦃G, L⦄ ⊢ ⓑ{a,I}V1.T1 ➡*[h, o] ⓑ{a,I}V2.T2. +(* Basic_2A1: was: cpxs_bind2 *) +lemma cpxs_bind_dx (h) (G): ∀L,V1,V2. ⦃G, L⦄ ⊢ V1 ⬈*[h] V2 → + ∀I,T1,T2. ⦃G, L.ⓑ{I}V2⦄ ⊢ T1 ⬈*[h] T2 → + ∀p. ⦃G, L⦄ ⊢ ⓑ{p,I}V1.T1 ⬈*[h] ⓑ{p,I}V2.T2. /4 width=5 by lpxs_cpxs_trans, lpxs_pair, cpxs_bind/ qed. -(* Inversion lemmas on context-sensitive ext parallel computation for terms *) +(* Inversion lemmas with context-sensitive ext rt-computation for terms *****) -lemma cpxs_inv_abst1: ∀h,o,a,G,L,V1,T1,U2. ⦃G, L⦄ ⊢ ⓛ{a}V1.T1 ➡*[h, o] U2 → - ∃∃V2,T2. ⦃G, L⦄ ⊢ V1 ➡*[h, o] V2 & ⦃G, L.ⓛV1⦄ ⊢ T1 ➡*[h, o] T2 & - U2 = ⓛ{a}V2.T2. -#h #o #a #G #L #V1 #T1 #U2 #H @(cpxs_ind … H) -U2 /2 width=5 by ex3_2_intro/ +lemma cpxs_inv_abst1 (h) (G): ∀p,L,V1,T1,U2. ⦃G, L⦄ ⊢ ⓛ{p}V1.T1 ⬈*[h] U2 → + ∃∃V2,T2. ⦃G, L⦄ ⊢ V1 ⬈*[h] V2 & ⦃G, L.ⓛV1⦄ ⊢ T1 ⬈*[h] T2 & + U2 = ⓛ{p}V2.T2. +#h #G #p #L #V1 #T1 #U2 #H @(cpxs_ind … H) -U2 /2 width=5 by ex3_2_intro/ #U0 #U2 #_ #HU02 * #V0 #T0 #HV10 #HT10 #H destruct elim (cpx_inv_abst1 … HU02) -HU02 #V2 #T2 #HV02 #HT02 #H destruct lapply (lpxs_cpx_trans … HT02 (L.ⓛV1) ?) /3 width=5 by lpxs_pair, cpxs_trans, cpxs_strap1, ex3_2_intro/ qed-. -lemma cpxs_inv_abbr1: ∀h,o,a,G,L,V1,T1,U2. ⦃G, L⦄ ⊢ ⓓ{a}V1.T1 ➡*[h, o] U2 → ( - ∃∃V2,T2. ⦃G, L⦄ ⊢ V1 ➡*[h, o] V2 & ⦃G, L.ⓓV1⦄ ⊢ T1 ➡*[h, o] T2 & - U2 = ⓓ{a}V2.T2 - ) ∨ - ∃∃T2. ⦃G, L.ⓓV1⦄ ⊢ T1 ➡*[h, o] T2 & ⬆[0, 1] U2 ≡ T2 & a = true. -#h #o #a #G #L #V1 #T1 #U2 #H @(cpxs_ind … H) -U2 /3 width=5 by ex3_2_intro, or_introl/ +(* Basic_2A1: was: cpxs_inv_abbr1 *) +lemma cpxs_inv_abbr1_dx (h) (p) (G) (L): + ∀V1,T1,U2. ⦃G, L⦄ ⊢ ⓓ{p}V1.T1 ⬈*[h] U2 → + ∨∨ ∃∃V2,T2. ⦃G, L⦄ ⊢ V1 ⬈*[h] V2 & ⦃G, L.ⓓV1⦄ ⊢ T1 ⬈*[h] T2 & + U2 = ⓓ{p}V2.T2 + | ∃∃T2. ⦃G, L.ⓓV1⦄ ⊢ T1 ⬈*[h] T2 & ⬆*[1] U2 ≘ T2 & p = Ⓣ. +#h #p #G #L #V1 #T1 #U2 #H +@(cpxs_ind … H) -U2 /3 width=5 by ex3_2_intro, or_introl/ #U0 #U2 #_ #HU02 * * [ #V0 #T0 #HV10 #HT10 #H destruct elim (cpx_inv_abbr1 … HU02) -HU02 * [ #V2 #T2 #HV02 #HT02 #H destruct lapply (lpxs_cpx_trans … HT02 (L.ⓓV1) ?) /4 width=5 by lpxs_pair, cpxs_trans, cpxs_strap1, ex3_2_intro, or_introl/ - | #T2 #HT02 #HUT2 - lapply (lpxs_cpx_trans … HT02 (L.ⓓV1) ?) -HT02 - /4 width=3 by lpxs_pair, cpxs_trans, ex3_intro, or_intror/ + | #T2 #HT20 #HTU2 #Hp -V0 + elim (cpx_lifts_sn … HTU2 (Ⓣ) … (L.ⓓV1) … HT20) -T2 [| /3 width=3 by drops_refl, drops_drop/ ] #U0 #HU20 #HTU0 + /4 width=3 by cpxs_strap1, ex3_intro, or_intror/ ] -| #U1 #HTU1 #HU01 - elim (lift_total U2 0 1) #U #HU2 - /6 width=12 by cpxs_strap1, cpx_lift, drop_drop, ex3_intro, or_intror/ -] -qed-. - -(* More advanced properties *************************************************) - -lemma lpxs_pair2: ∀h,o,I,G,L1,L2. ⦃G, L1⦄ ⊢ ➡*[h, o] L2 → - ∀V1,V2. ⦃G, L2⦄ ⊢ V1 ➡*[h, o] V2 → ⦃G, L1.ⓑ{I}V1⦄ ⊢ ➡*[h, o] L2.ⓑ{I}V2. -/3 width=3 by lpxs_pair, lpxs_cpxs_trans/ qed. - -(* Properties on supclosure *************************************************) - -lemma lpx_fqup_trans: ∀h,o,G1,G2,L1,L2,T1,T2. ⦃G1, L1, T1⦄ ⊐+ ⦃G2, L2, T2⦄ → - ∀K1. ⦃G1, K1⦄ ⊢ ➡[h, o] L1 → - ∃∃K2,T. ⦃G1, K1⦄ ⊢ T1 ➡*[h, o] T & ⦃G1, K1, T⦄ ⊐+ ⦃G2, K2, T2⦄ & ⦃G2, K2⦄ ⊢ ➡[h, o] L2. -#h #o #G1 #G2 #L1 #L2 #T1 #T2 #H @(fqup_ind … H) -G2 -L2 -T2 -[ #G2 #L2 #T2 #H12 #K1 #HKL1 elim (lpx_fqu_trans … H12 … HKL1) -L1 - /3 width=5 by cpx_cpxs, fqu_fqup, ex3_2_intro/ -| #G #G2 #L #L2 #T #T2 #_ #H2 #IH1 #K1 #HLK1 elim (IH1 … HLK1) -L1 - #L0 #T0 #HT10 #HT0 #HL0 elim (lpx_fqu_trans … H2 … HL0) -L - #L #T3 #HT3 #HT32 #HL2 elim (fqup_cpx_trans … HT0 … HT3) -T - /3 width=7 by cpxs_strap1, fqup_strap1, ex3_2_intro/ +| #U1 #HTU1 #HU01 #Hp + elim (cpx_lifts_sn … HU02 (Ⓣ) … (L.ⓓV1) … HU01) -U0 [| /3 width=3 by drops_refl, drops_drop/ ] #U #HU2 #HU1 + /4 width=3 by cpxs_strap1, ex3_intro, or_intror/ ] qed-. - -lemma lpx_fqus_trans: ∀h,o,G1,G2,L1,L2,T1,T2. ⦃G1, L1, T1⦄ ⊐* ⦃G2, L2, T2⦄ → - ∀K1. ⦃G1, K1⦄ ⊢ ➡[h, o] L1 → - ∃∃K2,T. ⦃G1, K1⦄ ⊢ T1 ➡*[h, o] T & ⦃G1, K1, T⦄ ⊐* ⦃G2, K2, T2⦄ & ⦃G2, K2⦄ ⊢ ➡[h, o] L2. -#h #o #G1 #G2 #L1 #L2 #T1 #T2 #H @(fqus_ind … H) -G2 -L2 -T2 [ /2 width=5 by ex3_2_intro/ ] -#G #G2 #L #L2 #T #T2 #_ #H2 #IH1 #K1 #HLK1 elim (IH1 … HLK1) -L1 -#L0 #T0 #HT10 #HT0 #HL0 elim (lpx_fquq_trans … H2 … HL0) -L -#L #T3 #HT3 #HT32 #HL2 elim (fqus_cpx_trans … HT0 … HT3) -T -/3 width=7 by cpxs_strap1, fqus_strap1, ex3_2_intro/ -qed-. - -lemma lpxs_fquq_trans: ∀h,o,G1,G2,L1,L2,T1,T2. ⦃G1, L1, T1⦄ ⊐⸮ ⦃G2, L2, T2⦄ → - ∀K1. ⦃G1, K1⦄ ⊢ ➡*[h, o] L1 → - ∃∃K2,T. ⦃G1, K1⦄ ⊢ T1 ➡*[h, o] T & ⦃G1, K1, T⦄ ⊐⸮ ⦃G2, K2, T2⦄ & ⦃G2, K2⦄ ⊢ ➡*[h, o] L2. -#h #o #G1 #G2 #L1 #L2 #T1 #T2 #HT12 #K1 #H @(lpxs_ind_dx … H) -K1 -[ /2 width=5 by ex3_2_intro/ -| #K1 #K #HK1 #_ * #L #T #HT1 #HT2 #HL2 -HT12 - lapply (lpx_cpxs_trans … HT1 … HK1) -HT1 - elim (lpx_fquq_trans … HT2 … HK1) -K - /3 width=7 by lpxs_strap2, cpxs_strap1, ex3_2_intro/ -] -qed-. - -lemma lpxs_fqup_trans: ∀h,o,G1,G2,L1,L2,T1,T2. ⦃G1, L1, T1⦄ ⊐+ ⦃G2, L2, T2⦄ → - ∀K1. ⦃G1, K1⦄ ⊢ ➡*[h, o] L1 → - ∃∃K2,T. ⦃G1, K1⦄ ⊢ T1 ➡*[h, o] T & ⦃G1, K1, T⦄ ⊐+ ⦃G2, K2, T2⦄ & ⦃G2, K2⦄ ⊢ ➡*[h, o] L2. -#h #o #G1 #G2 #L1 #L2 #T1 #T2 #HT12 #K1 #H @(lpxs_ind_dx … H) -K1 -[ /2 width=5 by ex3_2_intro/ -| #K1 #K #HK1 #_ * #L #T #HT1 #HT2 #HL2 -HT12 - lapply (lpx_cpxs_trans … HT1 … HK1) -HT1 - elim (lpx_fqup_trans … HT2 … HK1) -K - /3 width=7 by lpxs_strap2, cpxs_trans, ex3_2_intro/ -] -qed-. - -lemma lpxs_fqus_trans: ∀h,o,G1,G2,L1,L2,T1,T2. ⦃G1, L1, T1⦄ ⊐* ⦃G2, L2, T2⦄ → - ∀K1. ⦃G1, K1⦄ ⊢ ➡*[h, o] L1 → - ∃∃K2,T. ⦃G1, K1⦄ ⊢ T1 ➡*[h, o] T & ⦃G1, K1, T⦄ ⊐* ⦃G2, K2, T2⦄ & ⦃G2, K2⦄ ⊢ ➡*[h, o] L2. -#h #o #G1 #G2 #L1 #L2 #T1 #T2 #H @(fqus_ind … H) -G2 -L2 -T2 /2 width=5 by ex3_2_intro/ -#G #G2 #L #L2 #T #T2 #_ #H2 #IH1 #K1 #HLK1 elim (IH1 … HLK1) -L1 -#L0 #T0 #HT10 #HT0 #HL0 elim (lpxs_fquq_trans … H2 … HL0) -L -#L #T3 #HT3 #HT32 #HL2 elim (fqus_cpxs_trans … HT3 … HT0) -T -/3 width=7 by cpxs_trans, fqus_strap1, ex3_2_intro/ -qed-.