X-Git-Url: http://matita.cs.unibo.it/gitweb/?a=blobdiff_plain;f=matita%2Fmatita%2Fcontribs%2Flambdadelta%2Fbasic_2%2Frt_computation%2Fcprs.ma;h=4b221d5a4337107714d10449aa983a6c856c776e;hb=bd53c4e895203eb049e75434f638f26b5a161a2b;hp=af0618bc5ca95187024adf45a45209d4b03dbc4b;hpb=c53be14933feb896df2c3c9830b68fe773b2047c;p=helm.git diff --git a/matita/matita/contribs/lambdadelta/basic_2/rt_computation/cprs.ma b/matita/matita/contribs/lambdadelta/basic_2/rt_computation/cprs.ma index af0618bc5..4b221d5a4 100644 --- a/matita/matita/contribs/lambdadelta/basic_2/rt_computation/cprs.ma +++ b/matita/matita/contribs/lambdadelta/basic_2/rt_computation/cprs.ma @@ -15,16 +15,16 @@ include "basic_2/rt_transition/cpr.ma". include "basic_2/rt_computation/cpms.ma". -(* CONTEXT-SENSITIVE PARALLEL COMPUTATION FOR TERMS *************************) +(* CONTEXT-SENSITIVE PARALLEL R-COMPUTATION FOR TERMS ***********************) (* Basic eliminators ********************************************************) (* Basic_2A1: was: cprs_ind_dx *) -lemma cprs_ind_sn (h) (G) (L) (T2) (R:predicate …): - R T2 → - (∀T1,T. ⦃G, L⦄ ⊢ T1 ➡[h] T → ⦃G, L⦄ ⊢ T ➡*[h] T2 → R T → R T1) → - ∀T1. ⦃G, L⦄ ⊢ T1 ➡*[h] T2 → R T1. -#h #G #L #T2 #R #IH1 #IH2 #T1 +lemma cprs_ind_sn (h) (G) (L) (T2) (Q:predicate …): + Q T2 → + (∀T1,T. ❪G,L❫ ⊢ T1 ➡[h] T → ❪G,L❫ ⊢ T ➡*[h] T2 → Q T → Q T1) → + ∀T1. ❪G,L❫ ⊢ T1 ➡*[h] T2 → Q T1. +#h #G #L #T2 #Q #IH1 #IH2 #T1 @(insert_eq_0 … 0) #n #H @(cpms_ind_sn … H) -n -T1 // #n1 #n2 #T1 #T #HT1 #HT2 #IH #H @@ -33,11 +33,11 @@ elim (plus_inv_O3 n1 n2) // -H #H1 #H2 destruct qed-. (* Basic_2A1: was: cprs_ind *) -lemma cprs_ind_dx (h) (G) (L) (T1) (R:predicate …): - R T1 → - (∀T,T2. ⦃G, L⦄ ⊢ T1 ➡*[h] T → ⦃G, L⦄ ⊢ T ➡[h] T2 → R T → R T2) → - ∀T2. ⦃G, L⦄ ⊢ T1 ➡*[h] T2 → R T2. -#h #G #L #T1 #R #IH1 #IH2 #T2 +lemma cprs_ind_dx (h) (G) (L) (T1) (Q:predicate …): + Q T1 → + (∀T,T2. ❪G,L❫ ⊢ T1 ➡*[h] T → ❪G,L❫ ⊢ T ➡[h] T2 → Q T → Q T2) → + ∀T2. ❪G,L❫ ⊢ T1 ➡*[h] T2 → Q T2. +#h #G #L #T1 #Q #IH1 #IH2 #T2 @(insert_eq_0 … 0) #n #H @(cpms_ind_dx … H) -n -T2 // #n1 #n2 #T #T2 #HT1 #IH #HT2 #H @@ -50,75 +50,50 @@ qed-. (* Basic_1: was: pr3_step *) (* Basic_2A1: was: cprs_strap2 *) lemma cprs_step_sn (h) (G) (L): - ∀T1,T. ⦃G, L⦄ ⊢ T1 ➡[h] T → - ∀T2. ⦃G, L⦄ ⊢ T ➡*[h] T2 → ⦃G, L⦄ ⊢ T1 ➡*[h] T2. + ∀T1,T. ❪G,L❫ ⊢ T1 ➡[h] T → + ∀T2. ❪G,L❫ ⊢ T ➡*[h] T2 → ❪G,L❫ ⊢ T1 ➡*[h] T2. /2 width=3 by cpms_step_sn/ qed-. (* Basic_2A1: was: cprs_strap1 *) lemma cprs_step_dx (h) (G) (L): - ∀T1,T. ⦃G, L⦄ ⊢ T1 ➡*[h] T → - ∀T2. ⦃G, L⦄ ⊢ T ➡[h] T2 → ⦃G, L⦄ ⊢ T1 ➡*[h] T2. + ∀T1,T. ❪G,L❫ ⊢ T1 ➡*[h] T → + ∀T2. ❪G,L❫ ⊢ T ➡[h] T2 → ❪G,L❫ ⊢ T1 ➡*[h] T2. /2 width=3 by cpms_step_dx/ qed-. (* Basic_1: was only: pr3_thin_dx *) lemma cprs_flat_dx (h) (I) (G) (L): - ∀V1,V2. ⦃G, L⦄ ⊢ V1 ➡[h] V2 → - ∀T1,T2. ⦃G, L⦄ ⊢ T1 ➡*[h] T2 → - ⦃G, L⦄ ⊢ ⓕ{I}V1.T1 ➡*[h] ⓕ{I}V2.T2. + ∀V1,V2. ❪G,L❫ ⊢ V1 ➡[h] V2 → + ∀T1,T2. ❪G,L❫ ⊢ T1 ➡*[h] T2 → + ❪G,L❫ ⊢ ⓕ[I]V1.T1 ➡*[h] ⓕ[I]V2.T2. #h #I #G #L #V1 #V2 #HV12 #T1 #T2 #H @(cprs_ind_sn … H) -T1 /3 width=3 by cprs_step_sn, cpm_cpms, cpr_flat/ qed. -(* -lemma cprs_flat_sn: ∀I,G,L,T1,T2. ⦃G, L⦄ ⊢ T1 ➡[h] T2 → ∀V1,V2. ⦃G, L⦄ ⊢ V1 ➡*[h] V2 → - ⦃G, L⦄ ⊢ ⓕ{I} V1. T1 ➡*[h] ⓕ{I} V2. T2. -#I #G #L #T1 #T2 #HT12 #V1 #V2 #H @(cprs_ind … H) -V2 -/3 width=3 by cprs_strap1, cpr_cprs, cpr_pair_sn, cpr_flat/ -qed. - -lemma cprs_zeta: ∀G,L,V,T1,T,T2. ⬆[0, 1] T2 ≘ T → - ⦃G, L.ⓓV⦄ ⊢ T1 ➡*[h] T → ⦃G, L⦄ ⊢ +ⓓV.T1 ➡*[h] T2. -#G #L #V #T1 #T #T2 #HT2 #H @(cprs_ind_dx … H) -T1 -/3 width=3 by cprs_strap2, cpr_cprs, cpr_bind, cpr_zeta/ -qed. -lemma cprs_eps: ∀G,L,T1,T2. ⦃G, L⦄ ⊢ T1 ➡*[h] T2 → ∀V. ⦃G, L⦄ ⊢ ⓝV.T1 ➡*[h] T2. -#G #L #T1 #T2 #H @(cprs_ind … H) -T2 -/3 width=3 by cprs_strap1, cpr_cprs, cpr_eps/ -qed. - -lemma cprs_beta_dx: ∀a,G,L,V1,V2,W1,W2,T1,T2. - ⦃G, L⦄ ⊢ V1 ➡[h] V2 → ⦃G, L⦄ ⊢ W1 ➡[h] W2 → ⦃G, L.ⓛW1⦄ ⊢ T1 ➡*[h] T2 → - ⦃G, L⦄ ⊢ ⓐV1.ⓛ{a}W1.T1 ➡*[h] ⓓ{a}ⓝW2.V2.T2. -#a #G #L #V1 #V2 #W1 #W2 #T1 #T2 #HV12 #HW12 * -T2 -/4 width=7 by cprs_strap1, cpr_cprs, cprs_bind_dx, cprs_flat_dx, cpr_beta/ -qed. - -lemma cprs_theta_dx: ∀a,G,L,V1,V,V2,W1,W2,T1,T2. - ⦃G, L⦄ ⊢ V1 ➡[h] V → ⬆[0, 1] V ≘ V2 → ⦃G, L.ⓓW1⦄ ⊢ T1 ➡*[h] T2 → - ⦃G, L⦄ ⊢ W1 ➡[h] W2 → ⦃G, L⦄ ⊢ ⓐV1.ⓓ{a}W1.T1 ➡*[h] ⓓ{a}W2.ⓐV2.T2. -#a #G #L #V1 #V #V2 #W1 #W2 #T1 #T2 #HV1 #HV2 * -T2 -/4 width=9 by cprs_strap1, cpr_cprs, cprs_bind_dx, cprs_flat_dx, cpr_theta/ +lemma cprs_flat_sn (h) (I) (G) (L): + ∀T1,T2. ❪G,L❫ ⊢ T1 ➡[h] T2 → ∀V1,V2. ❪G,L❫ ⊢ V1 ➡*[h] V2 → + ❪G,L❫ ⊢ ⓕ[I] V1. T1 ➡*[h] ⓕ[I] V2. T2. +#h #I #G #L #T1 #T2 #HT12 #V1 #V2 #H @(cprs_ind_sn … H) -V1 +/3 width=3 by cprs_step_sn, cpm_cpms, cpr_flat/ qed. (* Basic inversion lemmas ***************************************************) (* Basic_1: was: pr3_gen_sort *) -lemma cprs_inv_sort1: ∀G,L,U2,s. ⦃G, L⦄ ⊢ ⋆s ➡*[h] U2 → U2 = ⋆s. -#G #L #U2 #s #H @(cprs_ind … H) -U2 // -#U2 #U #_ #HU2 #IHU2 destruct ->(cpr_inv_sort1 … HU2) -HU2 // -qed-. +lemma cprs_inv_sort1 (h) (G) (L): ∀X2,s. ❪G,L❫ ⊢ ⋆s ➡*[h] X2 → X2 = ⋆s. +/2 width=4 by cpms_inv_sort1/ qed-. (* Basic_1: was: pr3_gen_cast *) -lemma cprs_inv_cast1: ∀G,L,W1,T1,U2. ⦃G, L⦄ ⊢ ⓝW1.T1 ➡*[h] U2 → ⦃G, L⦄ ⊢ T1 ➡*[h] U2 ∨ - ∃∃W2,T2. ⦃G, L⦄ ⊢ W1 ➡*[h] W2 & ⦃G, L⦄ ⊢ T1 ➡*[h] T2 & U2 = ⓝW2.T2. -#G #L #W1 #T1 #U2 #H @(cprs_ind … H) -U2 /3 width=5 by ex3_2_intro, or_intror/ -#U2 #U #_ #HU2 * /3 width=3 by cprs_strap1, or_introl/ * -#W #T #HW1 #HT1 #H destruct -elim (cpr_inv_cast1 … HU2) -HU2 /3 width=3 by cprs_strap1, or_introl/ * -#W2 #T2 #HW2 #HT2 #H destruct /4 width=5 by cprs_strap1, ex3_2_intro, or_intror/ +lemma cprs_inv_cast1 (h) (G) (L): ∀W1,T1,X2. ❪G,L❫ ⊢ ⓝW1.T1 ➡*[h] X2 → + ∨∨ ∃∃W2,T2. ❪G,L❫ ⊢ W1 ➡*[h] W2 & ❪G,L❫ ⊢ T1 ➡*[h] T2 & X2 = ⓝW2.T2 + | ❪G,L❫ ⊢ T1 ➡*[h] X2. +#h #G #L #W1 #T1 #X2 #H +elim (cpms_inv_cast1 … H) -H +[ /2 width=1 by or_introl/ +| /2 width=1 by or_intror/ +| * #m #_ #H destruct +] qed-. -*) + (* Basic_1: removed theorems 13: pr1_head_1 pr1_head_2 pr1_comp clear_pr3_trans pr3_cflat pr3_gen_bind