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

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

diff --git a/matita/matita/contribs/lambdadelta/basic_2/computation/fsb_alt.ma b/matita/matita/contribs/lambdadelta/basic_2/computation/fsb_alt.ma
index 39b97103d64699b6e7c5c81e1ba6840232af0884..992775d70aac4e893ed96f0cf3243a1946212a96 100644 (file)
--- a/matita/matita/contribs/lambdadelta/basic_2/computation/fsb_alt.ma
+++ b/matita/matita/contribs/lambdadelta/basic_2/computation/fsb_alt.ma
@@ -13,7 +13,7 @@
 (**************************************************************************)
 
 include "basic_2/notation/relations/btsnalt_5.ma".
-include "basic_2/computation/fpbg.ma".
+include "basic_2/computation/fpbg_fpbg.ma".
 include "basic_2/computation/fsb.ma".
 
 (* "BIG TREE" STRONGLY NORMALIZING TERMS ************************************)
@@ -21,7 +21,7 @@ include "basic_2/computation/fsb.ma".
 (* Note: alternative definition of fsb *)
 inductive fsba (h) (g): relation3 genv lenv term ≝
 | fsba_intro: ∀G1,L1,T1. (
-                 ∀G2,L2,T2. ⦃G1, L1, T1⦄ >[h, g] ⦃G2, L2, T2⦄ → fsba h g G2 L2 T2
+                 ∀G2,L2,T2. ⦃G1, L1, T1⦄ >⋕[h, g] ⦃G2, L2, T2⦄ → fsba h g G2 L2 T2
               ) → fsba h g G1 L1 T1.
 
 interpretation
@@ -30,19 +30,54 @@ interpretation
 
 (* Basic eliminators ********************************************************)
 
-theorem fsba_ind_alt: ∀h,g. ∀R: relation3 …. (
-                         ∀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 fsba_ind_alt: ∀h,g. ∀R: relation3 …. (
+                       ∀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.
 #h #g #R #IH #G #L #T #H elim H -G -L -T
 /4 width=1 by fsba_intro/
 qed-.
 
+(* Basic properties *********************************************************)
+
+lemma fsba_fpbs_trans: ∀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 @(fsba_ind_alt … H) -G1 -L1 -T1
+/4 width=5 by fsba_intro, fpbs_fpbg_trans/
+qed-.
+
+(* Main properties **********************************************************)
+
+theorem fsb_fsba: ∀h,g,G,L,T. ⦃G, L⦄ ⊢ ⦥[h, g] T → ⦃G, L⦄ ⊢ ⦥⦥[h, g] T.
+#h #g #G #L #T #H @(fsb_ind_alt … H) -G -L -T
+#G1 #L1 #T1 #_ #IH @fsba_intro
+#G2 #L2 #T2 #H elim (fpbg_inv_fpbu_sn … H) -H
+/3 width=5 by fsba_fpbs_trans/
+qed.
+
 (* Main inversion lemmas ****************************************************)
 
 theorem fsba_inv_fsb: ∀h,g,G,L,T. ⦃G, L⦄ ⊢ ⦥⦥[h, g] T → ⦃G, L⦄ ⊢ ⦥[h, g] T.
 #h #g #G #L #T #H @(fsba_ind_alt … H) -G -L -T
-/4 width=1 by fsb_intro, fpbc_fpbg/
+/5 width=1 by fsb_intro, fpbc_fpbg, fpbu_fpbc/
+qed-.
+
+(* Advanced properties ******************************************************)
+
+lemma fsb_fpbs_trans: ∀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.
+/4 width=5 by fsba_inv_fsb, fsb_fsba, fsba_fpbs_trans/ qed-.
+
+(* Advanced eliminators *****************************************************)
+
+lemma fsb_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
+                    ) →
+                    ∀G1,L1,T1. ⦃G1, L1⦄ ⊢ ⦥[h, g] T1 → R G1 L1 T1.
+#h #g #R #IH #G1 #L1 #T1 #H @(fsba_ind_alt h g … G1 L1 T1)
+/3 width=1 by fsba_inv_fsb, fsb_fsba/
 qed-.