universary milestone in basic_2

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

diff --git a/matita/matita/contribs/lambdadelta/basic_2/computation/fsb_csx.ma b/matita/matita/contribs/lambdadelta/basic_2/computation/fsb_csx.ma
index f983e8d060f8aaf33c0f1e6835e505dc3f31a3e8..e86c302b8217c848917bcad34c3c9ee1e5105131 100644 (file)
--- a/matita/matita/contribs/lambdadelta/basic_2/computation/fsb_csx.ma
+++ b/matita/matita/contribs/lambdadelta/basic_2/computation/fsb_csx.ma
@@ -12,56 +12,59 @@
 (*                                                                        *)
 (**************************************************************************)
 
-include "basic_2/computation/fpbs_ext.ma".
+include "basic_2/computation/fpbs_fpb.ma".
+include "basic_2/computation/fpbs_fpbs.ma".
 include "basic_2/computation/csx_fpbs.ma".
 include "basic_2/computation/lsx_csx.ma".
 include "basic_2/computation/fsb_alt.ma".
 
-(* "BIG TREE" STRONGLY NORMALIZING TERMS ************************************)
+(* "QRST" STRONGLY NORMALIZING CLOSURES *************************************)
 
-(* Advanced propreties on context-senstive extended bormalizing terms *******)
+(* Advanced propreties on context-sensitive extended normalizing terms ******)
 
-lemma csx_fsb_fpbs: ∀h,g,G1,L1,T1. ⦃G1, L1⦄ ⊢ ⬊*[h, g] T1 →
-                    ∀G2,L2,T2. ⦃G1, L1, T1⦄ ≥[h, g] ⦃G2, L2, T2⦄ → ⦃G2, L2⦄ ⊢ ⦥[h, g] T2.
-#h #g #G1 #L1 #T1 #H @(csx_ind_alt … H) -T1
+lemma csx_fsb_fpbs: ∀h,o,G1,L1,T1. ⦃G1, L1⦄ ⊢ ⬊*[h, o] T1 →
+                    ∀G2,L2,T2. ⦃G1, L1, T1⦄ ≥[h, o] ⦃G2, L2, T2⦄ → ⦥[h, o] ⦃G2, L2, T2⦄.
+#h #o #G1 #L1 #T1 #H @(csx_ind … H) -T1
 #T1 #HT1 #IHc #G2 #L2 #T2 @(fqup_wf_ind … G2 L2 T2) -G2 -L2 -T2
 #G0 #L0 #T0 #IHu #H10 lapply (csx_fpbs_conf … H10) // -HT1
 #HT0 generalize in match IHu; -IHu generalize in match H10; -H10
 @(lsx_ind … (csx_lsx … HT0 0)) -L0
-#L0 #_ #IHl #H10 #IHu @fsb_intro
-#G2 #L2 #T2 * -G2 -L2 -T2 [ -IHl -IHc | -IHu -IHl |  ]
-[ /3 width=5 by fpbs_fqup_trans/
-| #T2 #HT02 #HnT02 elim (fpbs_cpxs_trans_neq … H10 … HT02 HnT02) -T0
+#L0 #_ #IHd #H10 #IHu @fsb_intro
+#G2 #L2 #T2 * -G2 -L2 -T2 [ -IHd -IHc | -IHu -IHd |  ]
+[ /4 width=5 by fpbs_fqup_trans, fqu_fqup/
+| #T2 #HT02 #HnT02 elim (fpbs_cpx_trans_neq … H10 … HT02 HnT02) -T0
   /3 width=4 by/
-| #L2 #HL02 #HnL02 @(IHl … HL02 HnL02) -IHl -HnL02 [ -IHu -IHc | ]
-  [ /2 width=3 by fpbs_lpxs_trans/
-  | #G3 #L3 #T3 #H03 #_ elim (lpxs_fqup_trans … H03 … HL02) -L2
+| #L2 #HL02 #HnL02 @(IHd … HL02 HnL02) -IHd -HnL02 [ -IHu -IHc | ]
+  [ /3 width=3 by fpbs_lpxs_trans, lpx_lpxs/
+  | #G3 #L3 #T3 #H03 #_ elim (lpx_fqup_trans … H03 … HL02) -L2
     #L4 #T4 elim (eq_term_dec T0 T4) [ -IHc | -IHu ]
-    [ #H destruct /4 width=5 by fsb_fpbs_trans, lpxs_fpbs, fpbs_fqup_trans/
-    | #HnT04 #HT04 #H04 elim (fpbs_cpxs_trans_neq … H10 … HT04 HnT04) -T0
-      /4 width=8 by fpbs_fqup_trans, fpbs_lpxs_trans/
+    [ #H destruct /5 width=5 by fsb_fpbs_trans, lpxs_fpbs, fpbs_fqup_trans, lpx_lpxs/
+    | #HnT04 #HT04 #H04 #HL43 elim (cpxs_neq_inv_step_sn … HT04 HnT04) -HT04 -HnT04
+      #T2 #HT02 #HnT02 #HT24 elim (fpbs_cpx_trans_neq … H10 … HT02 HnT02) -T0
+      lapply (fpbs_intro_alt … G3 … L4 … L3 L3 … T3 … HT24 ? ? ?) -HT24
+      /3 width=8 by fpbs_trans, lpx_lpxs, fqup_fqus/ (**) (* full auto too slow *)
     ]
   ]
 ]
 qed.
 
-lemma csx_fsb: ∀h,g,G,L,T. ⦃G, L⦄ ⊢ ⬊*[h, g] T → ⦃G, L⦄ ⊢ ⦥[h, g] T.
+lemma csx_fsb: ∀h,o,G,L,T. ⦃G, L⦄ ⊢ ⬊*[h, o] T → ⦥[h, o] ⦃G, L, T⦄.
 /2 width=5 by csx_fsb_fpbs/ qed.
 
 (* Advanced eliminators *****************************************************)
 
-lemma csx_ind_fpbu: ∀h,g. ∀R:relation3 genv lenv term.
-                    (∀G1,L1,T1. ⦃G1, L1⦄ ⊢ ⬊*[h, g] T1 →
-                                (∀G2,L2,T2. ⦃G1, L1, T1⦄ ≻[h, g] ⦃G2, L2, T2⦄ → R G2 L2 T2) →
-                                R G1 L1 T1
-                    ) →
-                    ∀G,L,T. ⦃G, L⦄ ⊢ ⬊*[h, g] T → R G L T.
+lemma csx_ind_fpb: ∀h,o. ∀R:relation3 genv lenv term.
+                   (∀G1,L1,T1. ⦃G1, L1⦄ ⊢ ⬊*[h, o] T1 →
+                               (∀G2,L2,T2. ⦃G1, L1, T1⦄ ≻[h, o] ⦃G2, L2, T2⦄ → R G2 L2 T2) →
+                               R G1 L1 T1
+                   ) →
+                   ∀G,L,T. ⦃G, L⦄ ⊢ ⬊*[h, o] T → R G L T.
 /4 width=4 by fsb_inv_csx, csx_fsb, fsb_ind_alt/ qed-.
 
-lemma csx_ind_fpbg: ∀h,g. ∀R:relation3 genv lenv term.
-                    (∀G1,L1,T1. ⦃G1, L1⦄ ⊢ ⬊*[h, g] T1 →
-                                (â\88\80G2,L2,T2. â¦\83G1, L1, T1â¦\84 >â\8b\95[h, g] ⦃G2, L2, T2⦄ → R G2 L2 T2) →
+lemma csx_ind_fpbg: ∀h,o. ∀R:relation3 genv lenv term.
+                    (∀G1,L1,T1. ⦃G1, L1⦄ ⊢ ⬊*[h, o] T1 →
+                                (â\88\80G2,L2,T2. â¦\83G1, L1, T1â¦\84 >â\89¡[h, o] ⦃G2, L2, T2⦄ → R G2 L2 T2) →
                                 R G1 L1 T1
                     ) →
-                    ∀G,L,T. ⦃G, L⦄ ⊢ ⬊*[h, g] T → R G L T.
+                    ∀G,L,T. ⦃G, L⦄ ⊢ ⬊*[h, o] T → R G L T.
 /4 width=4 by fsb_inv_csx, csx_fsb, fsb_ind_fpbg/ qed-.