- advances in the theory of cofrees

[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 f25939dd3d02c15211aaf2699eb807089bc8b250..41ba54fd303b194f2e7a472737dce4ae56443ffc 100644 (file)
--- a/matita/matita/contribs/lambdadelta/basic_2/computation/fsb_csx.ma
+++ b/matita/matita/contribs/lambdadelta/basic_2/computation/fsb_csx.ma
@@ -12,38 +12,42 @@
 (*                                                                        *)
 (**************************************************************************)
 
+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".
 
-axiom lsx_fqup_conf: ∀h,g,G1,G2,L1,L2,T1,T2. ⦃G1, L1, T1⦄ ⊃+ ⦃G2, L2, T2⦄ →
-                     G1 ⊢ ⋕⬊*[h, g, T1] L1 → G2 ⊢ ⋕⬊*[h, g, T2] L2.
-
-axiom fqup_lpxs_trans_nlleq: ∀h,g,G1,G2,K1,K2,T1,T2. ⦃G1, K1, T1⦄ ⊃+ ⦃G2, K2, T2⦄ →
-                             ∀L2. ⦃G2, K2⦄ ⊢ ➡*[h, g] L2 → (K2 ⋕[O, T2] L2 →⊥) →
-                             ∃∃L1. ⦃G1, K1⦄ ⊢ ➡*[h, g] L1 &
-                                   K1 ⋕[O, T1] L1 → ⊥ & ⦃G1, L1, T1⦄ ⊃+ ⦃G2, L2, T2⦄.
-
 (* "BIG TREE" STRONGLY NORMALIZING TERMS ************************************)
 
 (* Advanced propreties on context-senstive extended bormalizing terms *******)
 
-lemma csx_fsb: ∀h,g,G,L,T. ⦃G, L⦄ ⊢ ⬊*[h, g] T → ⦃G, L⦄ ⊢ ⦥[h, g] T.
+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 @(lsx_ind h g T1 G1 … L1) /2 width=1 by csx_lsx/ -L1
-#L1 @(fqup_wf_ind … G1 L1 T1) -G1 -L1 -T1
-#G1 #L1 #T1 #IHu #H1 #IHl #IHc @fsb_intro
-#G2 #L2 #T2 * -G2 -L2 -T2
-[ #G2 #L2 #T2 #H12 @IHu -IHu /2 width=5 by lsx_fqup_conf/ -H1 [| -IHl ]
-  [ #L0 #HL20 #HnL20 #_ elim (fqup_lpxs_trans_nlleq … H12 … HL20 HnL20) -L2
-    /6 width=5 by fsb_fpbs_trans, lpxs_fpbs, fqup_fpbs, lpxs_cpxs_trans/
-  | #T0 #HT20 #HnT20 elim (fqup_cpxs_trans_neq … H12 … HT20 HnT20) -T2
-    /4 width=5 by fsb_fpbs_trans, fqup_fpbs/
+#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/
+    ]
   ]
-| -H1 -IHu -IHl /3 width=1 by/
-| -H1 -IHu /5 width=5 by fsb_fpbs_trans, lpxs_fpbs, lpxs_cpxs_trans/
 ]
 qed.
 
+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.
@@ -56,7 +60,7 @@ lemma csx_ind_fpbu: ∀h,g. ∀R:relation3 genv lenv term.
 
 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) →
+                                (â\88\80G2,L2,T2. â¦\83G1, L1, T1â¦\84 >â\89¡[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.