- basic_2: reaxiomatized snv with improved cpds and cpes simplifies preservation

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

diff --git a/matita/matita/contribs/lambdadelta/basic_2/computation/cpds_cpds.ma b/matita/matita/contribs/lambdadelta/basic_2/computation/cpds_cpds.ma
index 9bd6b2d878e469aff3c137b4d651e1e336312257..d09fe1ebbdd0b2cc497f59d826be2d0022b171aa 100644 (file)
--- a/matita/matita/contribs/lambdadelta/basic_2/computation/cpds_cpds.ma
+++ b/matita/matita/contribs/lambdadelta/basic_2/computation/cpds_cpds.ma
@@ -21,55 +21,72 @@ include "basic_2/computation/cpds.ma".
 
 (* Advanced properties ******************************************************)
 
-lemma cpds_strap2: ∀h,g,G,L,T1,T,T2,l. ⦃G, L⦄ ⊢ T1 ▪[h, g] l+1 →
-                   ⦃G, L⦄ ⊢ T1 •[h] T → ⦃G, L⦄ ⊢ T •*➡*[h, g] T2 → ⦃G, L⦄ ⊢ T1 •*➡*[h, g] T2.
-#h #g #G #L #T1 #T #T2 #l #Hl #HT1 *
-#T0 #l0 #l1 #Hl10 #HT #HT0 #HT02
-lapply (da_sta_conf … HT1 … Hl) <minus_plus_m_m #H0T
-lapply (da_mono … H0T … HT) -HT -H0T #H destruct
-/3 width=7 by lstas_step_sn, le_S_S, ex4_3_intro/
+lemma cpds_strap2: ∀h,g,G,L,T1,T,T2,l1,l. ⦃G, L⦄ ⊢ T1 ▪[h, g] l1+1 →
+                   ⦃G, L⦄ ⊢ T1 •[h] T → ⦃G, L⦄ ⊢ T •*➡*[h, g, l] T2 →
+                   ⦃G, L⦄ ⊢ T1 •*➡*[h, g, l+1] T2.
+#h #g #G #L #T1 #T #T2 #l1 #l #Hl1 #HT1 *
+#T0 #l0 #Hl0 #HTl0 #HT0 #HT02
+lapply (da_sta_conf … HT1 … Hl1) <minus_plus_m_m #HTl1
+lapply (da_mono … HTl0 … HTl1) -HTl0 -HTl1 #H destruct
+/3 width=6 by lstas_step_sn, le_S_S, ex4_2_intro/
 qed.
 
-lemma cpds_cprs_trans: ∀h,g,G,L,T1,T,T2.
-                       ⦃G, L⦄ ⊢ T1 •*➡*[h, g] T → ⦃G, L⦄ ⊢ T ➡* T2 → ⦃G, L⦄ ⊢ T1 •*➡*[h, g] T2.
-#h #g #G #L #T1 #T #T2 * /3 width=9 by cprs_trans, ex4_3_intro/
+lemma cpds_cprs_trans: ∀h,g,G,L,T1,T,T2,l.
+                       ⦃G, L⦄ ⊢ T1 •*➡*[h, g, l] T → ⦃G, L⦄ ⊢ T ➡* T2 → ⦃G, L⦄ ⊢ T1 •*➡*[h, g, l] T2.
+#h #g #G #L #T1 #T #T2 #l * /3 width=8 by cprs_trans, ex4_2_intro/
 qed-.
 
-lemma lstas_cpds_trans: ∀h,g,G,L,T1,T,T2,l1,l2.
+lemma lstas_cpds_trans: ∀h,g,G,L,T1,T,T2,l1,l2,l.
                         l2 ≤ l1 → ⦃G, L⦄ ⊢ T1 ▪[h, g] l1 →
-                        ⦃G, L⦄ ⊢ T1 •*[h, l2] T → ⦃G, L⦄ ⊢ T •*➡*[h, g] T2 → ⦃G, L⦄ ⊢ T1 •*➡*[h, g] T2.
-#h #g #G #L #T1 #T #T2 #l1 #l2 #Hl21 #Hl1 #HT1 * #T0 #l3 #l4 #Hl43 #Hl3 #HT0 #HT02
-lapply (lstas_da_conf … HT1 … Hl1) #H0T
-lapply (da_mono … H0T … Hl3) -H0T -Hl3 #H destruct
-lapply (le_minus_to_plus_r … Hl21 Hl43) -Hl21 -Hl43
-/3 width=8 by lstas_trans, ex4_3_intro/
+                        ⦃G, L⦄ ⊢ T1 •*[h, l2] T → ⦃G, L⦄ ⊢ T •*➡*[h, g, l] T2 → ⦃G, L⦄ ⊢ T1 •*➡*[h, g, l2+l] T2.
+#h #g #G #L #T1 #T #T2 #l1 #l2 #l #Hl21 #HTl1 #HT1 * #T0 #l0 #Hl0 #HTl0 #HT0 #HT02
+lapply (lstas_da_conf … HT1 … HTl1) #HTl12
+lapply (da_mono … HTl12 … HTl0) -HTl12 -HTl0 #H destruct
+lapply (le_minus_to_plus_r … Hl21 Hl0) -Hl21 -Hl0
+/3 width=7 by lstas_trans, ex4_2_intro/
 qed-.
 
 (* Advanced inversion lemmas ************************************************)
 
-lemma cpds_inv_abst1: ∀h,g,a,G,L,V1,T1,U2. ⦃G, L⦄ ⊢ ⓛ{a}V1.T1 •*➡*[h, g] U2 →
-                      ∃∃V2,T2. ⦃G, L⦄ ⊢ V1 ➡* V2 & ⦃G, L.ⓛV1⦄ ⊢ T1 •*➡*[h, g] T2 &
+lemma cpds_inv_abst1: ∀h,g,a,G,L,V1,T1,U2,l. ⦃G, L⦄ ⊢ ⓛ{a}V1.T1 •*➡*[h, g, l] U2 →
+                      ∃∃V2,T2. ⦃G, L⦄ ⊢ V1 ➡* V2 & ⦃G, L.ⓛV1⦄ ⊢ T1 •*➡*[h, g, l] T2 &
                                U2 = ⓛ{a}V2.T2.
-#h #g #a #G #L #V1 #T1 #U2 * #X #l1 #l2 #Hl21 #Hl1 #H1 #H2
+#h #g #a #G #L #V1 #T1 #U2 #l2 * #X #l1 #Hl21 #Hl1 #H1 #H2
 lapply (da_inv_bind … Hl1) -Hl1 #Hl1
 elim (lstas_inv_bind1 … H1) -H1 #U #HTU1 #H destruct
 elim (cprs_inv_abst1 … H2) -H2 #V2 #T2 #HV12 #HUT2 #H destruct
-/3 width=7 by ex4_3_intro, ex3_2_intro/
+/3 width=6 by ex4_2_intro, ex3_2_intro/
 qed-.
 
-lemma cpds_inv_abbr_abst: ∀h,g,a1,a2,G,L,V1,W2,T1,T2. ⦃G, L⦄ ⊢ ⓓ{a1}V1.T1 •*➡*[h, g] ⓛ{a2}W2.T2 →
-                          ∃∃T. ⦃G, L.ⓓV1⦄ ⊢ T1 •*➡*[h, g] T & ⇧[0, 1] ⓛ{a2}W2.T2 ≡ T & a1 = true.
-#h #g #a1 #a2 #G #L #V1 #W2 #T1 #T2 * #X #l1 #l2 #Hl21 #Hl1 #H1 #H2
+lemma cpds_inv_abbr_abst: ∀h,g,a1,a2,G,L,V1,W2,T1,T2,l. ⦃G, L⦄ ⊢ ⓓ{a1}V1.T1 •*➡*[h, g, l] ⓛ{a2}W2.T2 →
+                          ∃∃T. ⦃G, L.ⓓV1⦄ ⊢ T1 •*➡*[h, g, l] T & ⇧[0, 1] ⓛ{a2}W2.T2 ≡ T & a1 = true.
+#h #g #a1 #a2 #G #L #V1 #W2 #T1 #T2 #l2 * #X #l1 #Hl21 #Hl1 #H1 #H2
 lapply (da_inv_bind … Hl1) -Hl1 #Hl1
 elim (lstas_inv_bind1 … H1) -H1 #U1 #HTU1 #H destruct
 elim (cprs_inv_abbr1 … H2) -H2 *
 [ #V2 #U2 #HV12 #HU12 #H destruct
-| /3 width=7 by ex4_3_intro, ex3_intro/
+| /3 width=6 by ex4_2_intro, ex3_intro/
 ]
 qed-.
 
+lemma cpds_inv_lstas_eq: ∀h,g,G,L,T1,T2,l. ⦃G, L⦄ ⊢ T1 •*➡*[h, g, l] T2 →
+                         ∀T. ⦃G, L⦄ ⊢ T1 •*[h, l] T → ⦃G, L⦄ ⊢ T ➡* T2.
+#h #g #G #L #T1 #T2 #l2 *
+#T0 #l1 #_ #_ #HT10 #HT02 #T #HT1
+lapply (lstas_mono … HT10 … HT1) #H destruct //
+qed-.
+
 (* Advanced forward lemmas **************************************************)
 
-lemma cpds_fwd_cpxs: ∀h,g,G,L,T1,T2. ⦃G, L⦄ ⊢ T1 •*➡*[h, g] T2 → ⦃G, L⦄ ⊢ T1 ➡*[h, g] T2.
-#h #g #G #L #T1 #T2 * /3 width=5 by cpxs_trans, lstas_cpxs, cprs_cpxs/
+lemma cpds_fwd_cpxs: ∀h,g,G,L,T1,T2,l. ⦃G, L⦄ ⊢ T1 •*➡*[h, g, l] T2 → ⦃G, L⦄ ⊢ T1 ➡*[h, g] T2.
+#h #g #G #L #T1 #T2 #l * /3 width=5 by cpxs_trans, lstas_cpxs, cprs_cpxs/
+qed-.
+
+(* Main properties **********************************************************)
+
+theorem cpds_conf_eq: ∀h,g,G,L,T0,T1,l. ⦃G, L⦄ ⊢ T0 •*➡*[h, g, l] T1 →
+                      ∀T2. ⦃G, L⦄ ⊢ T0 •*➡*[h, g, l] T2 →
+                      ∃∃T. ⦃G, L⦄ ⊢ T1 ➡* T & ⦃G, L⦄ ⊢ T2 ➡* T.
+#h #g #G #L #T0 #T1 #l0 * #U1 #l1 #_ #_ #H1 #HUT1 #T2 * #U2 #l2 #_ #_ #H2 #HUT2 -l1 -l2
+lapply (lstas_mono … H1 … H2) #H destruct -h -l0 /2 width=3 by cprs_conf/
 qed-.