partial commit: "computation" component ...

[helm.git] / matita / matita / contribs / lambdadelta / basic_2 / computation / csn.ma

diff --git a/matita/matita/contribs/lambdadelta/basic_2/computation/csn.ma b/matita/matita/contribs/lambdadelta/basic_2/computation/csn.ma
index e9eca96792bcf8ffd24dda4018d9ad298b1eb965..93d49b4fe4286c3a6c9e35be148aa1b0ea9aad17 100644 (file)
--- a/matita/matita/contribs/lambdadelta/basic_2/computation/csn.ma
+++ b/matita/matita/contribs/lambdadelta/basic_2/computation/csn.ma
@@ -12,41 +12,41 @@
 (*                                                                        *)
 (**************************************************************************)
 
-include "basic_2/notation/relations/sn_4.ma".
+include "basic_2/notation/relations/sn_5.ma".
 include "basic_2/reduction/cnx.ma".
 
 (* CONTEXT-SENSITIVE EXTENDED STRONGLY NORMALIZING TERMS ********************)
 
-definition csn: ∀h. sd h → lenv → predicate term ≝
-                λh,g,L. SN … (cpx h g L) (eq …).
+definition csn: ∀h. sd h → relation3 genv lenv term ≝
+                λh,g,G,L. SN … (cpx h g G L) (eq …).
 
 interpretation
    "context-sensitive extended strong normalization (term)"
-   'SN h g L T = (csn h g L T).
+   'SN h g G L T = (csn h g G L T).
 
 (* Basic eliminators ********************************************************)
 
-lemma csn_ind: ∀h,g,L. ∀R:predicate term.
+lemma csn_ind: ∀h,g,G,L. ∀R:predicate term.
                (∀T1. ⦃G, L⦄ ⊢ ⬊*[h, g] T1 →
                      (∀T2. ⦃G, L⦄ ⊢ T1 ➡[h, g] T2 → (T1 = T2 → ⊥) → R T2) →
                      R T1
                ) →
                ∀T. ⦃G, L⦄ ⊢ ⬊*[h, g] T → R T.
-#h #g #L #R #H0 #T1 #H elim H -T1 #T1 #HT1 #IHT1
+#h #g #G #L #R #H0 #T1 #H elim H -T1 #T1 #HT1 #IHT1
 @H0 -H0 /3 width=1/ -IHT1 /4 width=1/
 qed-.
 
 (* Basic properties *********************************************************)
 
 (* Basic_1: was just: sn3_pr2_intro *)
-lemma csn_intro: ∀h,g,L,T1.
+lemma csn_intro: ∀h,g,G,L,T1.
                  (∀T2. ⦃G, L⦄ ⊢ T1 ➡[h, g] T2 → (T1 = T2 → ⊥) → ⦃G, L⦄ ⊢ ⬊*[h, g] T2) →
                  ⦃G, L⦄ ⊢ ⬊*[h, g] T1.
 /4 width=1/ qed.
 
-lemma csn_cpx_trans: ∀h,g,L,T1. ⦃G, L⦄ ⊢ ⬊*[h, g] T1 →
+lemma csn_cpx_trans: ∀h,g,G,L,T1. ⦃G, L⦄ ⊢ ⬊*[h, g] T1 →
                      ∀T2. ⦃G, L⦄ ⊢ T1 ➡[h, g] T2 → ⦃G, L⦄ ⊢ ⬊*[h, g] T2.
-#h #g #L #T1 #H elim H -T1 #T1 #HT1 #IHT1 #T2 #HLT12
+#h #g #G #L #T1 #H elim H -T1 #T1 #HT1 #IHT1 #T2 #HLT12
 @csn_intro #T #HLT2 #HT2
 elim (term_eq_dec T1 T2) #HT12
 [ -IHT1 -HLT12 destruct /3 width=1/
@@ -54,11 +54,11 @@ elim (term_eq_dec T1 T2) #HT12
 qed-.
 
 (* Basic_1: was just: sn3_nf2 *)
-lemma cnx_csn: ∀h,g,L,T. ⦃G, L⦄ ⊢ 𝐍[h, g]⦃T⦄ → ⦃G, L⦄ ⊢ ⬊*[h, g] T.
+lemma cnx_csn: ∀h,g,G,L,T. ⦃G, L⦄ ⊢ 𝐍[h, g]⦃T⦄ → ⦃G, L⦄ ⊢ ⬊*[h, g] T.
 /2 width=1/ qed.
 
-lemma cnx_sort: ∀h,g,L,k. ⦃G, L⦄ ⊢ ⬊*[h, g] ⋆k.
-#h #g #L #k elim (deg_total h g k)
+lemma cnx_sort: ∀h,g,G,L,k. ⦃G, L⦄ ⊢ ⬊*[h, g] ⋆k.
+#h #g #G #L #k elim (deg_total h g k)
 #l generalize in match k; -k @(nat_ind_plus … l) -l /3 width=1/
 #l #IHl #k #Hkl lapply (deg_next_SO … Hkl) -Hkl
 #Hkl @csn_intro #X #H #HX elim (cpx_inv_sort1 … H) -H
@@ -68,9 +68,9 @@ lemma cnx_sort: ∀h,g,L,k. ⦃G, L⦄ ⊢ ⬊*[h, g] ⋆k.
 qed.
 
 (* Basic_1: was just: sn3_cast *)
-lemma csn_cast: ∀h,g,L,W. ⦃G, L⦄ ⊢ ⬊*[h, g] W →
+lemma csn_cast: ∀h,g,G,L,W. ⦃G, L⦄ ⊢ ⬊*[h, g] W →
                 ∀T. ⦃G, L⦄ ⊢ ⬊*[h, g] T → ⦃G, L⦄ ⊢ ⬊*[h, g] ⓝW.T.
-#h #g #L #W #HW @(csn_ind … HW) -W #W #HW #IHW #T #HT @(csn_ind … HT) -T #T #HT #IHT
+#h #g #G #L #W #HW @(csn_ind … HW) -W #W #HW #IHW #T #HT @(csn_ind … HT) -T #T #HT #IHT
 @csn_intro #X #H1 #H2
 elim (cpx_inv_cast1 … H1) -H1
 [ * #W0 #T0 #HLW0 #HLT0 #H destruct
@@ -84,37 +84,37 @@ qed.
 
 (* Basic forward lemmas *****************************************************)
 
-fact csn_fwd_pair_sn_aux: ∀h,g,L,U. ⦃G, L⦄ ⊢ ⬊*[h, g] U →
+fact csn_fwd_pair_sn_aux: ∀h,g,G,L,U. ⦃G, L⦄ ⊢ ⬊*[h, g] U →
                           ∀I,V,T. U = ②{I}V.T → ⦃G, L⦄ ⊢ ⬊*[h, g] V.
-#h #g #L #U #H elim H -H #U0 #_ #IH #I #V #T #H destruct
+#h #g #G #L #U #H elim H -H #U0 #_ #IH #I #V #T #H destruct
 @csn_intro #V2 #HLV2 #HV2
 @(IH (②{I}V2.T)) -IH // /2 width=1/ -HLV2 #H destruct /2 width=1/
 qed-.
 
 (* Basic_1: was just: sn3_gen_head *)
-lemma csn_fwd_pair_sn: ∀h,g,I,L,V,T. ⦃G, L⦄ ⊢ ⬊*[h, g] ②{I}V.T → ⦃G, L⦄ ⊢ ⬊*[h, g] V.
+lemma csn_fwd_pair_sn: ∀h,g,I,G,L,V,T. ⦃G, L⦄ ⊢ ⬊*[h, g] ②{I}V.T → ⦃G, L⦄ ⊢ ⬊*[h, g] V.
 /2 width=5 by csn_fwd_pair_sn_aux/ qed-.
 
-fact csn_fwd_bind_dx_aux: ∀h,g,L,U. ⦃G, L⦄ ⊢ ⬊*[h, g] U →
-                          ∀a,I,V,T. U = ⓑ{a,I}V.T → ⦃h, L.ⓑ{I}V⦄ ⊢ ⬊*[h, g] T.
-#h #g #L #U #H elim H -H #U0 #_ #IH #a #I #V #T #H destruct
+fact csn_fwd_bind_dx_aux: ∀h,g,G,L,U. ⦃G, L⦄ ⊢ ⬊*[h, g] U →
+                          ∀a,I,V,T. U = ⓑ{a,I}V.T → ⦃G, L.ⓑ{I}V⦄ ⊢ ⬊*[h, g] T.
+#h #g #G #L #U #H elim H -H #U0 #_ #IH #a #I #V #T #H destruct
 @csn_intro #T2 #HLT2 #HT2
-@(IH (ⓑ{a,I} V. T2)) -IH // /2 width=1/ -HLT2 #H destruct /2 width=1/
+@(IH (ⓑ{a,I}V.T2)) -IH // /2 width=1/ -HLT2 #H destruct /2 width=1/
 qed-.
 
 (* Basic_1: was just: sn3_gen_bind *)
-lemma csn_fwd_bind_dx: ∀h,g,a,I,L,V,T. ⦃G, L⦄ ⊢ ⬊*[h, g] ⓑ{a,I}V.T → ⦃h, L.ⓑ{I}V⦄ ⊢ ⬊*[h, g] T.
+lemma csn_fwd_bind_dx: ∀h,g,a,I,G,L,V,T. ⦃G, L⦄ ⊢ ⬊*[h, g] ⓑ{a,I}V.T → ⦃G, L.ⓑ{I}V⦄ ⊢ ⬊*[h, g] T.
 /2 width=4 by csn_fwd_bind_dx_aux/ qed-.
 
-fact csn_fwd_flat_dx_aux: ∀h,g,L,U. ⦃G, L⦄ ⊢ ⬊*[h, g] U →
+fact csn_fwd_flat_dx_aux: ∀h,g,G,L,U. ⦃G, L⦄ ⊢ ⬊*[h, g] U →
                           ∀I,V,T. U = ⓕ{I}V.T → ⦃G, L⦄ ⊢ ⬊*[h, g] T.
-#h #g #L #U #H elim H -H #U0 #_ #IH #I #V #T #H destruct
+#h #g #G #L #U #H elim H -H #U0 #_ #IH #I #V #T #H destruct
 @csn_intro #T2 #HLT2 #HT2
 @(IH (ⓕ{I}V.T2)) -IH // /2 width=1/ -HLT2 #H destruct /2 width=1/
 qed-.
 
 (* Basic_1: was just: sn3_gen_flat *)
-lemma csn_fwd_flat_dx: ∀h,g,I,L,V,T. ⦃G, L⦄ ⊢ ⬊*[h, g] ⓕ{I}V.T → ⦃G, L⦄ ⊢ ⬊*[h, g] T.
+lemma csn_fwd_flat_dx: ∀h,g,I,G,L,V,T. ⦃G, L⦄ ⊢ ⬊*[h, g] ⓕ{I}V.T → ⦃G, L⦄ ⊢ ⬊*[h, g] T.
 /2 width=5 by csn_fwd_flat_dx_aux/ qed-.
 
 (* Basic_1: removed theorems 14: