X-Git-Url: http://matita.cs.unibo.it/gitweb/?a=blobdiff_plain;f=matita%2Fmatita%2Fcontribs%2Flambdadelta%2Fbasic_2%2Frt_computation%2Flpxs_cpxs.ma;fp=matita%2Fmatita%2Fcontribs%2Flambdadelta%2Fbasic_2%2Frt_computation%2Flpxs_cpxs.ma;h=0000000000000000000000000000000000000000;hb=56dd0e9f60e0dabfb587b014755fd4dad27960bb;hp=6e1a9e2153316624928f75d7abcf7010a2377ef6;hpb=e866d78af74246133f5a14cb711a62af39308dee;p=helm.git 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 deleted file mode 100644 index 6e1a9e215..000000000 --- a/matita/matita/contribs/lambdadelta/basic_2/rt_computation/lpxs_cpxs.ma +++ /dev/null @@ -1,161 +0,0 @@ -(**************************************************************************) -(* ___ *) -(* ||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/computation/cpxs_cpxs.ma". -include "basic_2/computation/lpxs.ma". - -(* SN EXTENDED PARALLEL COMPUTATION ON LOCAL ENVIRONMENTS *******************) - -(* Advanced properties ******************************************************) - -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. -/4 width=5 by lpxs_cpxs_trans, lpxs_pair, cpxs_bind/ qed. - -(* Inversion lemmas on context-sensitive ext parallel 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/ -#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/ -#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/ - ] -| #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/ -] -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-.