update in basic_2

+ first results on cpms and cprs

diff --git a/matita/matita/contribs/lambdadelta/basic_2/rt_computation/cpms.ma b/matita/matita/contribs/lambdadelta/basic_2/rt_computation/cpms.ma
index cbfd28726da4b217c36efd0377120dc984680995..edb931591a9d69afc644c70cd099ef20bcc53496 100644 (file)
--- a/matita/matita/contribs/lambdadelta/basic_2/rt_computation/cpms.ma
+++ b/matita/matita/contribs/lambdadelta/basic_2/rt_computation/cpms.ma
@@ -31,8 +31,27 @@ interpretation
    "context-sensitive parallel r-computation (term)"
    'PRedStar h G L T1 T2 = (cpms h G L O T1 T2).
 
+(* Basic eliminators ********************************************************)
+
+lemma cpms_ind_sn (h) (G) (L) (T2) (Q:relation2 …):
+                  Q 0 T2 →
+                  (∀n1,n2,T1,T. ⦃G, L⦄ ⊢ T1 ➡[n1, h] T → ⦃G, L⦄ ⊢ T ➡*[n2, h] T2 → Q n2 T → Q (n1+n2) T1) →
+                  ∀n,T1. ⦃G, L⦄ ⊢ T1 ➡*[n, h] T2 → Q n T1.
+#h #G #L #T2 #R @ltc_ind_sn_refl //
+qed-.
+
+lemma cpms_ind_dx (h) (G) (L) (T1) (Q:relation2 …):
+                  Q 0 T1 →
+                  (∀n1,n2,T,T2. ⦃G, L⦄ ⊢ T1 ➡*[n1, h] T → Q n1 T → ⦃G, L⦄ ⊢ T ➡[n2, h] T2 → Q (n1+n2) T2) →
+                  ∀n,T2. ⦃G, L⦄ ⊢ T1 ➡*[n, h] T2 → Q n T2.
+#h #G #L #T1 #R @ltc_ind_dx_refl //
+qed-.
+
 (* Basic properties *********************************************************)
 
+(* Basic_1: includes: pr1_pr0 *)
+(* Basic_1: uses: pr3_pr2 *)
+(* Basic_2A1: includes: cpr_cprs *)
 lemma cpm_cpms (h) (G) (L): ∀n,T1,T2. ⦃G, L⦄ ⊢ T1 ➡[n, h] T2 → ⦃G, L⦄ ⊢ T1 ➡*[n, h] T2.
 /2 width=1 by ltc_rc/ qed.
 
@@ -44,27 +63,20 @@ lemma cpms_step_dx (h) (G) (L): ∀n1,T1,T. ⦃G, L⦄ ⊢ T1 ➡*[n1, h] T →
                                 ∀n2,T2. ⦃G, L⦄ ⊢ T ➡[n2, h] T2 → ⦃G, L⦄ ⊢ T1 ➡*[n1+n2, h] T2.
 /2 width=3 by ltc_dx/ qed-.
 
+(* Basic_2A1: uses: cprs_bind_dx *)
+lemma cpms_bind_dx (n) (h) (G) (L):
+                   ∀V1,V2. ⦃G, L⦄ ⊢ V1 ➡[h] V2 →
+                   ∀I,T1,T2. ⦃G, L.ⓑ{I}V1⦄ ⊢ T1 ➡*[n, h] T2 →
+                   ∀p. ⦃G, L⦄ ⊢ ⓑ{p,I}V1.T1 ➡*[n, h] ⓑ{p,I}V2.T2.
+#n #h #G #L #V1 #V2 #HV12 #I #T1 #T2 #H #a @(cpms_ind_sn … H) -T1
+/3 width=3 by cpms_step_sn, cpm_cpms, cpm_bind/ qed.
+
 (* Basic properties with r-transition ***************************************)
 
+(* Basic_1: was: pr3_refl *)
 lemma cprs_refl: ∀h,G,L. reflexive … (cpms h G L 0).
 /2 width=1 by cpm_cpms/ qed.
 
-(* Basic eliminators ********************************************************)
-
-lemma cpms_ind_sn (h) (G) (L) (T2) (Q:relation2 …):
-                  Q 0 T2 →
-                  (∀n1,n2,T1,T. ⦃G, L⦄ ⊢ T1 ➡[n1, h] T → ⦃G, L⦄ ⊢ T ➡*[n2, h] T2 → Q n2 T → Q (n1+n2) T1) →
-                  ∀n,T1. ⦃G, L⦄ ⊢ T1 ➡*[n, h] T2 → Q n T1.
-#h #G #L #T2 #R @ltc_ind_sn_refl //
-qed-.
-
-lemma cpms_ind_dx (h) (G) (L) (T1) (Q:relation2 …):
-                  Q 0 T1 →
-                  (∀n1,n2,T,T2. ⦃G, L⦄ ⊢ T1 ➡*[n1, h] T → Q n1 T → ⦃G, L⦄ ⊢ T ➡[n2, h] T2 → Q (n1+n2) T2) →
-                  ∀n,T2. ⦃G, L⦄ ⊢ T1 ➡*[n, h] T2 → Q n T2.
-#h #G #L #T1 #R @ltc_ind_dx_refl //
-qed-.
-
 (* Basic_2A1: removed theorems 4:
               sta_cprs_scpds lstas_scpds scpds_strap1 scpds_fwd_cprs
 *)

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 e4abc29d54d20328e22c236f2e552aef852c2dab..af0618bc5ca95187024adf45a45209d4b03dbc4b 100644 (file)
--- a/matita/matita/contribs/lambdadelta/basic_2/rt_computation/cprs.ma
+++ b/matita/matita/contribs/lambdadelta/basic_2/rt_computation/cprs.ma
@@ -12,100 +12,90 @@
 (*                                                                        *)
 (**************************************************************************)
 
-include "basic_2/notation/relations/predstar_4.ma".
-include "basic_2/reduction/cnr.ma".
+include "basic_2/rt_transition/cpr.ma".
+include "basic_2/rt_computation/cpms.ma".
 
-(* CONTEXT-SENSITIVE PARALLEL COMPUTATION ON TERMS **************************)
-
-(* Basic_1: includes: pr1_pr0 *)
-definition cprs: relation4 genv lenv term term ≝
-                 λG. CTC … (cpr G).
-
-interpretation "context-sensitive parallel computation (term)"
-   'PRedStar G L T1 T2 = (cprs G L T1 T2).
+(* CONTEXT-SENSITIVE PARALLEL COMPUTATION FOR TERMS *************************)
 
 (* Basic eliminators ********************************************************)
 
-lemma cprs_ind: ∀G,L,T1. ∀R:predicate term. R T1 →
-                (∀T,T2. ⦃G, L⦄ ⊢ T1 ➡* T → ⦃G, L⦄ ⊢ T ➡ T2 → R T → R T2) →
-                ∀T2. ⦃G, L⦄ ⊢ T1 ➡* T2 → R T2.
-#G #L #T1 #R #HT1 #IHT1 #T2 #HT12
-@(TC_star_ind … HT1 IHT1 … HT12) //
+(* 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
+@(insert_eq_0 … 0) #n #H
+@(cpms_ind_sn … H) -n -T1 //
+#n1 #n2 #T1 #T #HT1 #HT2 #IH #H
+elim (plus_inv_O3 n1 n2) // -H #H1 #H2 destruct
+/3 width=4 by/
 qed-.
 
-lemma cprs_ind_dx: ∀G,L,T2. ∀R:predicate term. R T2 →
-                   (∀T1,T. ⦃G, L⦄ ⊢ T1 ➡ T → ⦃G, L⦄ ⊢ T ➡* T2 → R T → R T1) →
-                   ∀T1. ⦃G, L⦄ ⊢ T1 ➡* T2 → R T1.
-#G #L #T2 #R #HT2 #IHT2 #T1 #HT12
-@(TC_star_ind_dx … HT2 IHT2 … HT12) //
+(* 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
+@(insert_eq_0 … 0) #n #H
+@(cpms_ind_dx … H) -n -T2 //
+#n1 #n2 #T #T2 #HT1 #IH #HT2 #H
+elim (plus_inv_O3 n1 n2) // -H #H1 #H2 destruct
+/3 width=4 by/
 qed-.
 
 (* Basic properties *********************************************************)
 
-(* Basic_1: was: pr3_pr2 *)
-lemma cpr_cprs: ∀G,L,T1,T2. ⦃G, L⦄ ⊢ T1 ➡ T2 → ⦃G, L⦄ ⊢ T1 ➡* T2.
-/2 width=1 by inj/ qed.
-
-(* Basic_1: was: pr3_refl *)
-lemma cprs_refl: ∀G,L,T. ⦃G, L⦄ ⊢ T ➡* T.
-/2 width=1 by cpr_cprs/ qed.
-
-lemma cprs_strap1: ∀G,L,T1,T,T2.
-                   ⦃G, L⦄ ⊢ T1 ➡* T → ⦃G, L⦄ ⊢ T ➡ T2 → ⦃G, L⦄ ⊢ T1 ➡* T2.
-normalize /2 width=3 by step/ qed-.
-
 (* Basic_1: was: pr3_step *)
-lemma cprs_strap2: ∀G,L,T1,T,T2.
-                   ⦃G, L⦄ ⊢ T1 ➡ T → ⦃G, L⦄ ⊢ T ➡* T2 → ⦃G, L⦄ ⊢ T1 ➡* T2.
-normalize /2 width=3 by TC_strap/ qed-.
-
-lemma lsubr_cprs_trans: ∀G. lsub_trans … (cprs G) lsubr.
-/3 width=5 by lsubr_cpr_trans, CTC_lsub_trans/
-qed-.
-
-(* Basic_1: was: pr3_pr1 *)
-lemma tprs_cprs: ∀G,L,T1,T2. ⦃G, ⋆⦄ ⊢ T1 ➡* T2 → ⦃G, L⦄ ⊢ T1 ➡* T2.
-/2 width=3 by lsubr_cprs_trans/ qed.
-
-lemma cprs_bind_dx: ∀G,L,V1,V2. ⦃G, L⦄ ⊢ V1 ➡ V2 → ∀I,T1,T2. ⦃G, L.ⓑ{I}V1⦄ ⊢ T1 ➡* T2 →
-                    ∀a. ⦃G, L⦄ ⊢ ⓑ{a,I}V1. T1 ➡* ⓑ{a,I}V2. T2.
-#G #L #V1 #V2 #HV12 #I #T1 #T2 #HT12 #a @(cprs_ind_dx … HT12) -T1
-/3 width=3 by cprs_strap2, cpr_cprs, cpr_pair_sn, cpr_bind/ qed.
+(* 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.
+/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.
+/2 width=3 by cpms_step_dx/ qed-.
 
 (* Basic_1: was only: pr3_thin_dx *)
-lemma cprs_flat_dx: ∀I,G,L,V1,V2. ⦃G, L⦄ ⊢ V1 ➡ V2 → ∀T1,T2. ⦃G, L⦄ ⊢ T1 ➡* T2 →
-                    ⦃G, L⦄ ⊢ ⓕ{I} V1. T1 ➡* ⓕ{I} V2. T2.
-#I #G #L #V1 #V2 #HV12 #T1 #T2 #HT12 @(cprs_ind … HT12) -T2
-/3 width=5 by cprs_strap1, cpr_flat, cpr_cprs, cpr_pair_sn/
+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.
+#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 ➡ T2 → ∀V1,V2. ⦃G, L⦄ ⊢ V1 ➡* V2 →
-                    ⦃G, L⦄ ⊢ ⓕ{I} V1. T1 ➡* ⓕ{I} V2. T2.
+(*
+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 ➡* T → ⦃G, L⦄ ⊢ +ⓓV.T1 ➡* T2.
+                 ⦃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 ➡* T2 → ∀V. ⦃G, L⦄ ⊢ ⓝV.T1 ➡* T2.
+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 ➡ V2 → ⦃G, L⦄ ⊢ W1 ➡ W2 → ⦃G, L.ⓛW1⦄ ⊢ T1 ➡* T2 →
-                    ⦃G, L⦄ ⊢ ⓐV1.ⓛ{a}W1.T1 ➡* ⓓ{a}ⓝW2.V2.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 ➡ V → ⬆[0, 1] V ≘ V2 → ⦃G, L.ⓓW1⦄ ⊢ T1 ➡* T2 →
-                     ⦃G, L⦄ ⊢ W1 ➡ W2 → ⦃G, L⦄ ⊢ ⓐV1.ⓓ{a}W1.T1 ➡* ⓓ{a}W2.ⓐV2.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/
 qed.
@@ -113,29 +103,22 @@ qed.
 (* Basic inversion lemmas ***************************************************)
 
 (* Basic_1: was: pr3_gen_sort *)
-lemma cprs_inv_sort1: ∀G,L,U2,s. ⦃G, L⦄ ⊢ ⋆s ➡* U2 → U2 = ⋆s.
+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-.
 
 (* Basic_1: was: pr3_gen_cast *)
-lemma cprs_inv_cast1: ∀G,L,W1,T1,U2. ⦃G, L⦄ ⊢ ⓝW1.T1 ➡* U2 → ⦃G, L⦄ ⊢ T1 ➡* U2 ∨
-                      ∃∃W2,T2. ⦃G, L⦄ ⊢ W1 ➡* W2 & ⦃G, L⦄ ⊢ T1 ➡* T2 & U2 = ⓝW2.T2.
+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/
 qed-.
-
-(* Basic_1: was: nf2_pr3_unfold *)
-lemma cprs_inv_cnr1: ∀G,L,T,U. ⦃G, L⦄ ⊢ T ➡* U → ⦃G, L⦄ ⊢ ➡ 𝐍⦃T⦄ → T = U.
-#G #L #T #U #H @(cprs_ind_dx … H) -T //
-#T0 #T #H1T0 #_ #IHT #H2T0
-lapply (H2T0 … H1T0) -H1T0 #H destruct /2 width=1 by/
-qed-.
-
+*)
 (* Basic_1: removed theorems 13:
    pr1_head_1 pr1_head_2 pr1_comp
    clear_pr3_trans pr3_cflat pr3_gen_bind

diff --git a/matita/matita/contribs/lambdadelta/basic_2/rt_computation/cprs_etc.ma b/matita/matita/contribs/lambdadelta/basic_2/rt_computation/cprs_etc.ma
new file mode 100644 (file)
index 0000000..2542616
--- /dev/null
+++ b/matita/matita/contribs/lambdadelta/basic_2/rt_computation/cprs_etc.ma
@@ -0,0 +1,14 @@
+lemma lsubr_cprs_trans: ∀G. lsub_trans … (cprs G) lsubr.
+/3 width=5 by lsubr_cpr_trans, CTC_lsub_trans/
+qed-.
+
+(* Basic_1: was: pr3_pr1 *)
+lemma tprs_cprs: ∀G,L,T1,T2. ⦃G, ⋆⦄ ⊢ T1 ➡* T2 → ⦃G, L⦄ ⊢ T1 ➡* T2.
+/2 width=3 by lsubr_cprs_trans/ qed.
+
+(* Basic_1: was: nf2_pr3_unfold *)
+lemma cprs_inv_cnr1: ∀G,L,T,U. ⦃G, L⦄ ⊢ T ➡* U → ⦃G, L⦄ ⊢ ➡ 𝐍⦃T⦄ → T = U.
+#G #L #T #U #H @(cprs_ind_dx … H) -T //
+#T0 #T #H1T0 #_ #IHT #H2T0
+lapply (H2T0 … H1T0) -H1T0 #H destruct /2 width=1 by/
+qed-.

diff --git a/matita/matita/contribs/lambdadelta/basic_2/rt_computation/partial.txt b/matita/matita/contribs/lambdadelta/basic_2/rt_computation/partial.txt
index 24215a06542e5346f61572b098e6cc600d7514eb..163c752ff202abf9cd3f034c9ed6f6e85fe21987 100644 (file)
--- a/matita/matita/contribs/lambdadelta/basic_2/rt_computation/partial.txt
+++ b/matita/matita/contribs/lambdadelta/basic_2/rt_computation/partial.txt
@@ -10,3 +10,4 @@ fpbs.ma fpbs_fqup.ma fpbs_fqus.ma fpbs_aaa.ma fpbs_cpx.ma fpbs_fpb.ma fpbs_cpxs.
 fpbg.ma fpbg_fqup.ma fpbg_cpxs.ma fpbg_lfpxs.ma fpbg_fpbs.ma fpbg_fpbg.ma
 fsb.ma fsb_ffdeq.ma fsb_aaa.ma fsb_csx.ma fsb_fpbg.ma
 cpms.ma
+cprs.ma