universary milestone in basic_2

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

diff --git a/matita/matita/contribs/lambdadelta/basic_2/computation/fpbs_lift.ma b/matita/matita/contribs/lambdadelta/basic_2/computation/fpbs_lift.ma
index 809bd3358cbe14bcf0186ec8f226f105d9ac2da6..69f1a77fa4b0ddc8949976ec336f2e4ccf8970f2 100644 (file)
--- a/matita/matita/contribs/lambdadelta/basic_2/computation/fpbs_lift.ma
+++ b/matita/matita/contribs/lambdadelta/basic_2/computation/fpbs_lift.ma
@@ -12,19 +12,25 @@
 (*                                                                        *)
 (**************************************************************************)
 
-include "basic_2/unfold/lsstas_lift.ma".
+include "basic_2/computation/cpxs_lift.ma".
 include "basic_2/computation/fpbs.ma".
 
-(* "BIG TREE" PARALLEL COMPUTATION FOR CLOSURES *****************************)
+(* "QRST" PARALLEL COMPUTATION FOR CLOSURES *********************************)
 
 (* Advanced properties ******************************************************)
 
-lemma lsstas_fpbs: ∀h,g,G,L,T1,T2,l2. ⦃G, L⦄ ⊢ T1 •*[h, g, l2] T2 →
-                   ∀l1. l2 ≤ l1 → ⦃G, L⦄ ⊢ T1 ▪[h, g] l1 → ⦃G, L, T1⦄ ≥[h, g] ⦃G, L, T2⦄.
-#h #g #G #L #T1 #T2 #l2 #H @(lsstas_ind_dx … H) -l2 -T2 //
-#l2 #T #T2 #HT1 #HT2 #IHT1 #l1 >commutative_plus #Hl21 #Hl1
-elim (le_inv_plus_l … Hl21) -Hl21 #Hl12 #Hl21
-lapply (lsstas_da_conf … HT1 … Hl1) -HT1
->(plus_minus_m_m … Hl12) -Hl12
-/3 width=5 by fpb_ssta, fpbs_strap1/
-qed.
+lemma lstas_fpbs: ∀h,o,G,L,T1,T2,d2. ⦃G, L⦄ ⊢ T1 •*[h, d2] T2 →
+                  ∀d1. d2 ≤ d1 → ⦃G, L⦄ ⊢ T1 ▪[h, o] d1 → ⦃G, L, T1⦄ ≥[h, o] ⦃G, L, T2⦄.
+/3 width=5 by cpxs_fpbs, lstas_cpxs/ qed.
+
+lemma sta_fpbs: ∀h,o,G,L,T,U,d.
+                ⦃G, L⦄ ⊢ T ▪[h, o] d+1 → ⦃G, L⦄ ⊢ T •*[h, 1] U →
+                ⦃G, L, T⦄ ≥[h, o] ⦃G, L, U⦄.
+/2 width=5 by lstas_fpbs/ qed.
+
+(* Note: this is used in the closure proof *)
+lemma cpr_lpr_sta_fpbs: ∀h,o,G,L1,L2,T1,T2,U2,d2.
+                        ⦃G, L1⦄ ⊢ T1 ➡ T2 → ⦃G, L1⦄ ⊢ ➡ L2 →
+                        ⦃G, L2⦄ ⊢ T2 ▪[h, o] d2+1 → ⦃G, L2⦄ ⊢ T2 •*[h, 1] U2 →
+                        ⦃G, L1, T1⦄ ≥[h, o] ⦃G, L2, U2⦄.
+/4 width=5 by fpbs_strap1, cpr_lpr_fpbs, sta_cpx, fpbq_cpx/ qed.