- "big tree" theorem is now proved up to some conjectures involving

[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..f25939dd3d02c15211aaf2699eb807089bc8b250 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 +12,52 @@
 (*                                                                        *)
 (**************************************************************************)
 
-include "basic_2/computation/csx_aaa.ma".
-include "basic_2/computation/fsb.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 ******************************************************)
+(* 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.
-#h #g #G #L #T #H @(csx_ind_fpbc … H) -T /3 width=1 by fsb_intro/
+#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/
+  ]
+| -H1 -IHu -IHl /3 width=1 by/
+| -H1 -IHu /5 width=5 by fsb_fpbs_trans, lpxs_fpbs, lpxs_cpxs_trans/
+]
 qed.
 
-(* Main properties **********************************************************)
+(* 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-.