- commit of the "s_computation" component ...

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

diff --git a/matita/matita/contribs/lambdadelta/basic_2/computation/scpds_scpds.ma b/matita/matita/contribs/lambdadelta/basic_2/computation/scpds_scpds.ma
index e9afcf4efe2f8fabacbe05235e386fd93bdbf5e2..6c5de0687db8f4adccd043b4e73095e1783b858a 100644 (file)
--- a/matita/matita/contribs/lambdadelta/basic_2/computation/scpds_scpds.ma
+++ b/matita/matita/contribs/lambdadelta/basic_2/computation/scpds_scpds.ma
@@ -21,26 +21,26 @@ include "basic_2/computation/scpds.ma".
 
 (* Advanced properties ******************************************************)
 
-lemma scpds_strap2: ∀h,g,G,L,T1,T,T2,d1,d. ⦃G, L⦄ ⊢ T1 ▪[h, g] d1+1 →
-                    ⦃G, L⦄ ⊢ T1 •*[h, 1] T → ⦃G, L⦄ ⊢ T •*➡*[h, g, d] T2 →
-                    ⦃G, L⦄ ⊢ T1 •*➡*[h, g, d+1] T2.
-#h #g #G #L #T1 #T #T2 #d1 #d #Hd1 #HT1 *
+lemma scpds_strap2: ∀h,o,G,L,T1,T,T2,d1,d. ⦃G, L⦄ ⊢ T1 ▪[h, o] d1+1 →
+                    ⦃G, L⦄ ⊢ T1 •*[h, 1] T → ⦃G, L⦄ ⊢ T •*➡*[h, o, d] T2 →
+                    ⦃G, L⦄ ⊢ T1 •*➡*[h, o, d+1] T2.
+#h #o #G #L #T1 #T #T2 #d1 #d #Hd1 #HT1 *
 #T0 #d0 #Hd0 #HTd0 #HT0 #HT02
-lapply (lstas_da_conf … HT1 … Hd1) <minus_plus_m_m #HTd1
+lapply (lstas_da_conf … HT1 … Hd1) <minus_plus_k_k #HTd1
 lapply (da_mono … HTd0 … HTd1) -HTd0 -HTd1 #H destruct
 lapply (lstas_trans … HT1 … HT0) -T >commutative_plus
 /3 width=6 by le_S_S, ex4_2_intro/
 qed.
 
-lemma scpds_cprs_trans: ∀h,g,G,L,T1,T,T2,d.
-                        ⦃G, L⦄ ⊢ T1 •*➡*[h, g, d] T → ⦃G, L⦄ ⊢ T ➡* T2 → ⦃G, L⦄ ⊢ T1 •*➡*[h, g, d] T2.
-#h #g #G #L #T1 #T #T2 #d * /3 width=8 by cprs_trans, ex4_2_intro/
+lemma scpds_cprs_trans: ∀h,o,G,L,T1,T,T2,d.
+                        ⦃G, L⦄ ⊢ T1 •*➡*[h, o, d] T → ⦃G, L⦄ ⊢ T ➡* T2 → ⦃G, L⦄ ⊢ T1 •*➡*[h, o, d] T2.
+#h #o #G #L #T1 #T #T2 #d * /3 width=8 by cprs_trans, ex4_2_intro/
 qed-.
 
-lemma lstas_scpds_trans: ∀h,g,G,L,T1,T,T2,d1,d2,d.
-                         d2 ≤ d1 → ⦃G, L⦄ ⊢ T1 ▪[h, g] d1 →
-                         ⦃G, L⦄ ⊢ T1 •*[h, d2] T → ⦃G, L⦄ ⊢ T •*➡*[h, g, d] T2 → ⦃G, L⦄ ⊢ T1 •*➡*[h, g, d2+d] T2.
-#h #g #G #L #T1 #T #T2 #d1 #d2 #d #Hd21 #HTd1 #HT1 * #T0 #d0 #Hd0 #HTd0 #HT0 #HT02
+lemma lstas_scpds_trans: ∀h,o,G,L,T1,T,T2,d1,d2,d.
+                         d2 ≤ d1 → ⦃G, L⦄ ⊢ T1 ▪[h, o] d1 →
+                         ⦃G, L⦄ ⊢ T1 •*[h, d2] T → ⦃G, L⦄ ⊢ T •*➡*[h, o, d] T2 → ⦃G, L⦄ ⊢ T1 •*➡*[h, o, d2+d] T2.
+#h #o #G #L #T1 #T #T2 #d1 #d2 #d #Hd21 #HTd1 #HT1 * #T0 #d0 #Hd0 #HTd0 #HT0 #HT02
 lapply (lstas_da_conf … HT1 … HTd1) #HTd12
 lapply (da_mono … HTd12 … HTd0) -HTd12 -HTd0 #H destruct
 lapply (le_minus_to_plus_r … Hd21 Hd0) -Hd21 -Hd0
@@ -49,19 +49,19 @@ qed-.
 
 (* Advanced inversion lemmas ************************************************)
 
-lemma scpds_inv_abst1: ∀h,g,a,G,L,V1,T1,U2,d. ⦃G, L⦄ ⊢ ⓛ{a}V1.T1 •*➡*[h, g, d] U2 →
-                       ∃∃V2,T2. ⦃G, L⦄ ⊢ V1 ➡* V2 & ⦃G, L.ⓛV1⦄ ⊢ T1 •*➡*[h, g, d] T2 &
+lemma scpds_inv_abst1: ∀h,o,a,G,L,V1,T1,U2,d. ⦃G, L⦄ ⊢ ⓛ{a}V1.T1 •*➡*[h, o, d] U2 →
+                       ∃∃V2,T2. ⦃G, L⦄ ⊢ V1 ➡* V2 & ⦃G, L.ⓛV1⦄ ⊢ T1 •*➡*[h, o, d] T2 &
                                 U2 = ⓛ{a}V2.T2.
-#h #g #a #G #L #V1 #T1 #U2 #d2 * #X #d1 #Hd21 #Hd1 #H1 #H2
+#h #o #a #G #L #V1 #T1 #U2 #d2 * #X #d1 #Hd21 #Hd1 #H1 #H2
 lapply (da_inv_bind … Hd1) -Hd1 #Hd1
 elim (lstas_inv_bind1 … H1) -H1 #U #HTU1 #H destruct
 elim (cprs_inv_abst1 … H2) -H2 #V2 #T2 #HV12 #HUT2 #H destruct
 /3 width=6 by ex4_2_intro, ex3_2_intro/
 qed-.
 
-lemma scpds_inv_abbr_abst: ∀h,g,a1,a2,G,L,V1,W2,T1,T2,d. ⦃G, L⦄ ⊢ ⓓ{a1}V1.T1 •*➡*[h, g, d] ⓛ{a2}W2.T2 →
-                           ∃∃T. ⦃G, L.ⓓV1⦄ ⊢ T1 •*➡*[h, g, d] T & ⬆[0, 1] ⓛ{a2}W2.T2 ≡ T & a1 = true.
-#h #g #a1 #a2 #G #L #V1 #W2 #T1 #T2 #d2 * #X #d1 #Hd21 #Hd1 #H1 #H2
+lemma scpds_inv_abbr_abst: ∀h,o,a1,a2,G,L,V1,W2,T1,T2,d. ⦃G, L⦄ ⊢ ⓓ{a1}V1.T1 •*➡*[h, o, d] ⓛ{a2}W2.T2 →
+                           ∃∃T. ⦃G, L.ⓓV1⦄ ⊢ T1 •*➡*[h, o, d] T & ⬆[0, 1] ⓛ{a2}W2.T2 ≡ T & a1 = true.
+#h #o #a1 #a2 #G #L #V1 #W2 #T1 #T2 #d2 * #X #d1 #Hd21 #Hd1 #H1 #H2
 lapply (da_inv_bind … Hd1) -Hd1 #Hd1
 elim (lstas_inv_bind1 … H1) -H1 #U1 #HTU1 #H destruct
 elim (cprs_inv_abbr1 … H2) -H2 *
@@ -70,24 +70,24 @@ elim (cprs_inv_abbr1 … H2) -H2 *
 ]
 qed-.
 
-lemma scpds_inv_lstas_eq: ∀h,g,G,L,T1,T2,d. ⦃G, L⦄ ⊢ T1 •*➡*[h, g, d] T2 →
+lemma scpds_inv_lstas_eq: ∀h,o,G,L,T1,T2,d. ⦃G, L⦄ ⊢ T1 •*➡*[h, o, d] T2 →
                           ∀T. ⦃G, L⦄ ⊢ T1 •*[h, d] T → ⦃G, L⦄ ⊢ T ➡* T2.
-#h #g #G #L #T1 #T2 #d2 *
+#h #o #G #L #T1 #T2 #d2 *
 #T0 #d1 #_ #_ #HT10 #HT02 #T #HT1
 lapply (lstas_mono … HT10 … HT1) #H destruct //
 qed-.
 
 (* Advanced forward lemmas **************************************************)
 
-lemma scpds_fwd_cpxs: ∀h,g,G,L,T1,T2,d. ⦃G, L⦄ ⊢ T1 •*➡*[h, g, d] T2 → ⦃G, L⦄ ⊢ T1 ➡*[h, g] T2.
-#h #g #G #L #T1 #T2 #d * /3 width=5 by cpxs_trans, lstas_cpxs, cprs_cpxs/
+lemma scpds_fwd_cpxs: ∀h,o,G,L,T1,T2,d. ⦃G, L⦄ ⊢ T1 •*➡*[h, o, d] T2 → ⦃G, L⦄ ⊢ T1 ➡*[h, o] T2.
+#h #o #G #L #T1 #T2 #d * /3 width=5 by cpxs_trans, lstas_cpxs, cprs_cpxs/
 qed-.
 
 (* Main properties **********************************************************)
 
-theorem scpds_conf_eq: ∀h,g,G,L,T0,T1,d. ⦃G, L⦄ ⊢ T0 •*➡*[h, g, d] T1 →
-                       ∀T2. ⦃G, L⦄ ⊢ T0 •*➡*[h, g, d] T2 →
+theorem scpds_conf_eq: ∀h,o,G,L,T0,T1,d. ⦃G, L⦄ ⊢ T0 •*➡*[h, o, d] T1 →
+                       ∀T2. ⦃G, L⦄ ⊢ T0 •*➡*[h, o, d] T2 →
                        ∃∃T. ⦃G, L⦄ ⊢ T1 ➡* T & ⦃G, L⦄ ⊢ T2 ➡* T.
-#h #g #G #L #T0 #T1 #d0 * #U1 #d1 #_ #_ #H1 #HUT1 #T2 * #U2 #d2 #_ #_ #H2 #HUT2 -d1 -d2
+#h #o #G #L #T0 #T1 #d0 * #U1 #d1 #_ #_ #H1 #HUT1 #T2 * #U2 #d2 #_ #_ #H2 #HUT2 -d1 -d2
 lapply (lstas_mono … H1 … H2) #H destruct -h -d0 /2 width=3 by cprs_conf/
 qed-.