X-Git-Url: http://matita.cs.unibo.it/gitweb/?a=blobdiff_plain;f=matita%2Fmatita%2Fcontribs%2Flambdadelta%2Fbasic_2%2Fcomputation%2Fcpxs_cpxs.ma;h=f25909b757436e51a8b667bfd6c4ec42d0c2d56a;hb=82500a9ceb53e1af0263c22afbd5954fa3a83190;hp=8958323296e1c68538e3f96df123682204ebdaef;hpb=8ed01fd6a38bea715ceb449bb7b72a46bad87851;p=helm.git diff --git a/matita/matita/contribs/lambdadelta/basic_2/computation/cpxs_cpxs.ma b/matita/matita/contribs/lambdadelta/basic_2/computation/cpxs_cpxs.ma index 895832329..f25909b75 100644 --- a/matita/matita/contribs/lambdadelta/basic_2/computation/cpxs_cpxs.ma +++ b/matita/matita/contribs/lambdadelta/basic_2/computation/cpxs_cpxs.ma @@ -12,75 +12,75 @@ (* *) (**************************************************************************) -include "basic_2/reduction/lpx_ldrop.ma". include "basic_2/computation/cpxs_lift.ma". +include "basic_2/reduction/lpx_ldrop.ma". (**) (* disambiguation error *) (* CONTEXT-SENSITIVE EXTENDED PARALLEL COMPUTATION ON TERMS *****************) (* Main properties **********************************************************) -theorem cpxs_trans: ∀h,g,L. Transitive … (cpxs h g L). -#h #g #L #T1 #T #HT1 #T2 @trans_TC @HT1 qed-. (**) (* auto /3 width=3/ does not work because a δ-expansion gets in the way *) +theorem cpxs_trans: ∀h,g,G,L. Transitive … (cpxs h g G L). +#h #g #G #L #T1 #T #HT1 #T2 @trans_TC @HT1 qed-. (**) (* auto /3 width=3/ does not work because a δ-expansion gets in the way *) -theorem cpxs_bind: ∀h,g,a,I,L,V1,V2,T1,T2. ⦃h, L.ⓑ{I}V1⦄ ⊢ T1 ➡*[h, g] T2 → +theorem cpxs_bind: ∀h,g,a,I,G,L,V1,V2,T1,T2. ⦃G, L.ⓑ{I}V1⦄ ⊢ T1 ➡*[h, g] T2 → ⦃G, L⦄ ⊢ V1 ➡*[h, g] V2 → ⦃G, L⦄ ⊢ ⓑ{a,I}V1.T1 ➡*[h, g] ⓑ{a,I}V2.T2. -#h #g #a #I #L #V1 #V2 #T1 #T2 #HT12 #H @(cpxs_ind … H) -V2 /2 width=1/ +#h #g #a #I #G #L #V1 #V2 #T1 #T2 #HT12 #H @(cpxs_ind … H) -V2 /2 width=1/ #V #V2 #_ #HV2 #IHV1 @(cpxs_trans … IHV1) -V1 /2 width=1/ qed. -theorem cpxs_flat: ∀h,g,I,L,V1,V2,T1,T2. ⦃G, L⦄ ⊢ T1 ➡*[h, g] T2 → +theorem cpxs_flat: ∀h,g,I,G,L,V1,V2,T1,T2. ⦃G, L⦄ ⊢ T1 ➡*[h, g] T2 → ⦃G, L⦄ ⊢ V1 ➡*[h, g] V2 → - ⦃G, L⦄ ⊢ ⓕ{I} V1.T1 ➡*[h, g] ⓕ{I} V2.T2. -#h #g #I #L #V1 #V2 #T1 #T2 #HT12 #H @(cpxs_ind … H) -V2 /2 width=1/ + ⦃G, L⦄ ⊢ ⓕ{I}V1.T1 ➡*[h, g] ⓕ{I}V2.T2. +#h #g #I #G #L #V1 #V2 #T1 #T2 #HT12 #H @(cpxs_ind … H) -V2 /2 width=1/ #V #V2 #_ #HV2 #IHV1 @(cpxs_trans … IHV1) -IHV1 /2 width=1/ qed. -theorem cpxs_beta_rc: ∀h,g,a,L,V1,V2,W1,W2,T1,T2. - ⦃G, L⦄ ⊢ V1 ➡[h, g] V2 → ⦃h, L.ⓛW1⦄ ⊢ T1 ➡*[h, g] T2 → ⦃G, L⦄ ⊢ W1 ➡*[h, g] W2 → +theorem cpxs_beta_rc: ∀h,g,a,G,L,V1,V2,W1,W2,T1,T2. + ⦃G, L⦄ ⊢ V1 ➡[h, g] V2 → ⦃G, L.ⓛW1⦄ ⊢ T1 ➡*[h, g] T2 → ⦃G, L⦄ ⊢ W1 ➡*[h, g] W2 → ⦃G, L⦄ ⊢ ⓐV1.ⓛ{a}W1.T1 ➡*[h, g] ⓓ{a}ⓝW2.V2.T2. -#h #g #a #L #V1 #V2 #W1 #W2 #T1 #T2 #HV12 #HT12 #H @(cpxs_ind … H) -W2 /2 width=1/ +#h #g #a #G #L #V1 #V2 #W1 #W2 #T1 #T2 #HV12 #HT12 #H @(cpxs_ind … H) -W2 /2 width=1/ #W #W2 #_ #HW2 #IHW1 @(cpxs_trans … IHW1) -IHW1 /3 width=1/ qed. -theorem cpxs_beta: ∀h,g,a,L,V1,V2,W1,W2,T1,T2. - ⦃h, L.ⓛW1⦄ ⊢ T1 ➡*[h, g] T2 → ⦃G, L⦄ ⊢ W1 ➡*[h, g] W2 → ⦃G, L⦄ ⊢ V1 ➡*[h, g] V2 → +theorem cpxs_beta: ∀h,g,a,G,L,V1,V2,W1,W2,T1,T2. + ⦃G, L.ⓛW1⦄ ⊢ T1 ➡*[h, g] T2 → ⦃G, L⦄ ⊢ W1 ➡*[h, g] W2 → ⦃G, L⦄ ⊢ V1 ➡*[h, g] V2 → ⦃G, L⦄ ⊢ ⓐV1.ⓛ{a}W1.T1 ➡*[h, g] ⓓ{a}ⓝW2.V2.T2. -#h #g #a #L #V1 #V2 #W1 #W2 #T1 #T2 #HT12 #HW12 #H @(cpxs_ind … H) -V2 /2 width=1/ +#h #g #a #G #L #V1 #V2 #W1 #W2 #T1 #T2 #HT12 #HW12 #H @(cpxs_ind … H) -V2 /2 width=1/ #V #V2 #_ #HV2 #IHV1 @(cpxs_trans … IHV1) -IHV1 /3 width=1/ qed. -theorem cpxs_theta_rc: ∀h,g,a,L,V1,V,V2,W1,W2,T1,T2. +theorem cpxs_theta_rc: ∀h,g,a,G,L,V1,V,V2,W1,W2,T1,T2. ⦃G, L⦄ ⊢ V1 ➡[h, g] V → ⇧[0, 1] V ≡ V2 → - ⦃h, L.ⓓW1⦄ ⊢ T1 ➡*[h, g] T2 → ⦃G, L⦄ ⊢ W1 ➡*[h, g] W2 → + ⦃G, L.ⓓW1⦄ ⊢ T1 ➡*[h, g] T2 → ⦃G, L⦄ ⊢ W1 ➡*[h, g] W2 → ⦃G, L⦄ ⊢ ⓐV1.ⓓ{a}W1.T1 ➡*[h, g] ⓓ{a}W2.ⓐV2.T2. -#h #g #a #L #V1 #V #V2 #W1 #W2 #T1 #T2 #HV1 #HV2 #HT12 #H elim H -W2 /2 width=3/ +#h #g #a #G #L #V1 #V #V2 #W1 #W2 #T1 #T2 #HV1 #HV2 #HT12 #H elim H -W2 /2 width=3/ #W #W2 #_ #HW2 #IHW1 @(cpxs_trans … IHW1) -IHW1 /2 width=1/ qed. -theorem cpxs_theta: ∀h,g,a,L,V1,V,V2,W1,W2,T1,T2. +theorem cpxs_theta: ∀h,g,a,G,L,V1,V,V2,W1,W2,T1,T2. ⇧[0, 1] V ≡ V2 → ⦃G, L⦄ ⊢ W1 ➡*[h, g] W2 → - ⦃h, L.ⓓW1⦄ ⊢ T1 ➡*[h, g] T2 → ⦃G, L⦄ ⊢ V1 ➡*[h, g] V → + ⦃G, L.ⓓW1⦄ ⊢ T1 ➡*[h, g] T2 → ⦃G, L⦄ ⊢ V1 ➡*[h, g] V → ⦃G, L⦄ ⊢ ⓐV1.ⓓ{a}W1.T1 ➡*[h, g] ⓓ{a}W2.ⓐV2.T2. -#h #g #a #L #V1 #V #V2 #W1 #W2 #T1 #T2 #HV2 #HW12 #HT12 #H @(TC_ind_dx … V1 H) -V1 /2 width=3/ +#h #g #a #G #L #V1 #V #V2 #W1 #W2 #T1 #T2 #HV2 #HW12 #HT12 #H @(TC_ind_dx … V1 H) -V1 /2 width=3/ #V1 #V0 #HV10 #_ #IHV0 @(cpxs_trans … IHV0) -IHV0 /2 width=1/ qed. (* Advanced inversion lemmas ************************************************) -lemma cpxs_inv_appl1: ∀h,g,L,V1,T1,U2. ⦃G, L⦄ ⊢ ⓐV1.T1 ➡*[h, g] U2 → +lemma cpxs_inv_appl1: ∀h,g,G,L,V1,T1,U2. ⦃G, L⦄ ⊢ ⓐV1.T1 ➡*[h, g] U2 → ∨∨ ∃∃V2,T2. ⦃G, L⦄ ⊢ V1 ➡*[h, g] V2 & ⦃G, L⦄ ⊢ T1 ➡*[h, g] T2 & U2 = ⓐV2. T2 | ∃∃a,W,T. ⦃G, L⦄ ⊢ T1 ➡*[h, g] ⓛ{a}W.T & ⦃G, L⦄ ⊢ ⓓ{a}ⓝW.V1.T ➡*[h, g] U2 | ∃∃a,V0,V2,V,T. ⦃G, L⦄ ⊢ V1 ➡*[h, g] V0 & ⇧[0,1] V0 ≡ V2 & ⦃G, L⦄ ⊢ T1 ➡*[h, g] ⓓ{a}V.T & ⦃G, L⦄ ⊢ ⓓ{a}V.ⓐV2.T ➡*[h, g] U2. -#h #g #L #V1 #T1 #U2 #H @(cpxs_ind … H) -U2 [ /3 width=5/ ] +#h #g #G #L #V1 #T1 #U2 #H @(cpxs_ind … H) -U2 [ /3 width=5/ ] #U #U2 #_ #HU2 * * [ #V0 #T0 #HV10 #HT10 #H destruct elim (cpx_inv_appl1 … HU2) -HU2 * @@ -99,42 +99,42 @@ qed-. (* Properties on sn extended parallel reduction for local environments ******) -lemma lpx_cpx_trans: ∀h,g. s_r_trans … (cpx h g) (lpx h g). -#h #g #L2 #T1 #T2 #HT12 elim HT12 -L2 -T1 -T2 +lemma lpx_cpx_trans: ∀h,g,G. s_r_trans … (cpx h g G) (lpx h g G). +#h #g #G #L2 #T1 #T2 #HT12 elim HT12 -G -L2 -T1 -T2 [ /2 width=3/ | /3 width=2/ -| #I #L2 #K2 #V0 #V2 #W2 #i #HLK2 #_ #HVW2 #IHV02 #L1 #HL12 +| #I #G #L2 #K2 #V0 #V2 #W2 #i #HLK2 #_ #HVW2 #IHV02 #L1 #HL12 elim (lpx_ldrop_trans_O1 … HL12 … HLK2) -L2 #X #HLK1 #H elim (lpx_inv_pair2 … H) -H #K1 #V1 #HK12 #HV10 #H destruct lapply (IHV02 … HK12) -K2 #HV02 lapply (cpxs_strap2 … HV10 … HV02) -V0 /2 width=7/ -| #a #I #L2 #V1 #V2 #T1 #T2 #_ #_ #IHV12 #IHT12 #L1 #HL12 +| #a #I #G #L2 #V1 #V2 #T1 #T2 #_ #_ #IHV12 #IHT12 #L1 #HL12 lapply (IHT12 (L1.ⓑ{I}V1) ?) -IHT12 /2 width=1/ /3 width=1/ |5,7,8: /3 width=1/ -| #L2 #V2 #T1 #T #T2 #_ #HT2 #IHT1 #L1 #HL12 +| #G #L2 #V2 #T1 #T #T2 #_ #HT2 #IHT1 #L1 #HL12 lapply (IHT1 (L1.ⓓV2) ?) -IHT1 /2 width=1/ /2 width=3/ -| #a #L2 #V1 #V2 #W1 #W2 #T1 #T2 #_ #_ #_ #IHV12 #IHW12 #IHT12 #L1 #HL12 +| #a #G #L2 #V1 #V2 #W1 #W2 #T1 #T2 #_ #_ #_ #IHV12 #IHW12 #IHT12 #L1 #HL12 lapply (IHT12 (L1.ⓛW1) ?) -IHT12 /2 width=1/ /3 width=1/ -| #a #L2 #V1 #V #V2 #W1 #W2 #T1 #T2 #_ #HV2 #_ #_ #IHV1 #IHW12 #IHT12 #L1 #HL12 +| #a #G #L2 #V1 #V #V2 #W1 #W2 #T1 #T2 #_ #HV2 #_ #_ #IHV1 #IHW12 #IHT12 #L1 #HL12 lapply (IHT12 (L1.ⓓW1) ?) -IHT12 /2 width=1/ /3 width=3/ ] qed-. -lemma cpx_bind2: ∀h,g,L,V1,V2. ⦃G, L⦄ ⊢ V1 ➡[h, g] V2 → - ∀I,T1,T2. ⦃h, L.ⓑ{I}V2⦄ ⊢ T1 ➡[h, g] T2 → +lemma cpx_bind2: ∀h,g,G,L,V1,V2. ⦃G, L⦄ ⊢ V1 ➡[h, g] V2 → + ∀I,T1,T2. ⦃G, L.ⓑ{I}V2⦄ ⊢ T1 ➡[h, g] T2 → ∀a. ⦃G, L⦄ ⊢ ⓑ{a,I}V1.T1 ➡*[h, g] ⓑ{a,I}V2.T2. -#h #g #L #V1 #V2 #HV12 #I #T1 #T2 #HT12 +#h #g #G #L #V1 #V2 #HV12 #I #T1 #T2 #HT12 lapply (lpx_cpx_trans … HT12 (L.ⓑ{I}V1) ?) /2 width=1/ qed. (* Advanced properties ******************************************************) -lemma lpx_cpxs_trans: ∀h,g. s_rs_trans … (cpx h g) (lpx h g). +lemma lpx_cpxs_trans: ∀h,g,G. s_rs_trans … (cpx h g G) (lpx h g G). /3 width=5 by s_r_trans_TC1, lpx_cpx_trans/ qed-. -lemma cpxs_bind2_dx: ∀h,g,L,V1,V2. ⦃G, L⦄ ⊢ V1 ➡[h, g] V2 → - ∀I,T1,T2. ⦃h, L.ⓑ{I}V2⦄ ⊢ T1 ➡*[h, g] T2 → +lemma cpxs_bind2_dx: ∀h,g,G,L,V1,V2. ⦃G, L⦄ ⊢ V1 ➡[h, g] V2 → + ∀I,T1,T2. ⦃G, L.ⓑ{I}V2⦄ ⊢ T1 ➡*[h, g] T2 → ∀a. ⦃G, L⦄ ⊢ ⓑ{a,I}V1.T1 ➡*[h, g] ⓑ{a,I}V2.T2. -#h #g #L #V1 #V2 #HV12 #I #T1 #T2 #HT12 +#h #g #G #L #V1 #V2 #HV12 #I #T1 #T2 #HT12 lapply (lpx_cpxs_trans … HT12 (L.ⓑ{I}V1) ?) /2 width=1/ qed.