refactoring to park the notions:

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

diff --git a/matita/matita/contribs/lambdadelta/basic_2/rt_computation/fsb_csx.ma b/matita/matita/contribs/lambdadelta/basic_2/rt_computation/fsb_csx.ma
new file mode 100644 (file)
index 0000000..e86c302
--- /dev/null
+++ b/matita/matita/contribs/lambdadelta/basic_2/rt_computation/fsb_csx.ma
@@ -0,0 +1,70 @@
+(**************************************************************************)
+(*       ___                                                              *)
+(*      ||M||                                                             *)
+(*      ||A||       A project by Andrea Asperti                           *)
+(*      ||T||                                                             *)
+(*      ||I||       Developers:                                           *)
+(*      ||T||         The HELM team.                                      *)
+(*      ||A||         http://helm.cs.unibo.it                             *)
+(*      \   /                                                             *)
+(*       \ /        This file is distributed under the terms of the       *)
+(*        v         GNU General Public License Version 2                  *)
+(*                                                                        *)
+(**************************************************************************)
+
+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".
+
+(* "QRST" STRONGLY NORMALIZING CLOSURES *************************************)
+
+(* Advanced propreties on context-sensitive extended normalizing terms ******)
+
+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 #_ #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 @(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 /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,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_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,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_fpbg/ qed-.