some renaming and some typos corrected ...

[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 6b1e14497ab35efde04983478a18ebfe3f9ba8d9..5941916f8696ffc64070cbcdcee43b68f9844aa6 100644 (file)
--- a/matita/matita/contribs/lambdadelta/basic_2/computation/fsb_csx.ma
+++ b/matita/matita/contribs/lambdadelta/basic_2/computation/fsb_csx.ma
@@ -12,19 +12,56 @@
 (*                                                                        *)
 (**************************************************************************)
 
-include "basic_2/computation/csx_aaa.ma".
-include "basic_2/computation/fsb.ma".
+include "basic_2/computation/fpbs_ext.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 ************************************)
 
-(* Advanced propreties ******************************************************)
+(* Advanced propreties on context-sensitive extended normalizing terms *******)
 
-lemma csx_fsb: ∀h,g,G,L,T. ⦃G, L⦄ ⊢ ⬊*[h, g] T → ⦃G, L⦄ ⊢ ⦥[h, g] T.
-#h #g #G #L #T #H @(csx_ind_fpbc … H) -T /3 width=1 by fsb_intro/
+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
+#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_alt … (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
+  /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
+    #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/
+    ]
+  ]
+]
 qed.
 
-(* Main properties **********************************************************)
+lemma csx_fsb: ∀h,g,G,L,T. ⦃G, L⦄ ⊢ ⬊*[h, g] T → ⦃G, L⦄ ⊢ ⦥[h, g] 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.
+/4 width=4 by fsb_inv_csx, csx_fsb, fsb_ind_alt/ qed-.
 
-(* Note: this is the "big tree" theorem ("small step" version) *)
-theorem aaa_fsb: ∀h,g,G,L,T,A. ⦃G, L⦄ ⊢ T ⁝ A → ⦃G, L⦄ ⊢ ⦥[h, g] T.
-/3 width=2 by aaa_csx, csx_fsb/ qed.
+lemma csx_ind_fpbg: ∀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.
+/4 width=4 by fsb_inv_csx, csx_fsb, fsb_ind_fpbg/ qed-.