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

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

diff --git a/matita/matita/contribs/lambdadelta/basic_2/computation/fsb.ma b/matita/matita/contribs/lambdadelta/basic_2/computation/fsb.ma
index 6c24fe86b35e664af61b63b74c9a62e717979d4a..1616402dec981972dba696ee60e6fe0405a57dc0 100644 (file)
--- a/matita/matita/contribs/lambdadelta/basic_2/computation/fsb.ma
+++ b/matita/matita/contribs/lambdadelta/basic_2/computation/fsb.ma
@@ -13,8 +13,8 @@
 (**************************************************************************)
 
 include "basic_2/notation/relations/btsn_5.ma".
-include "basic_2/reduction/fpbc.ma".
-include "basic_2/computation/csx.ma".
+include "basic_2/computation/fpbu.ma".
+include "basic_2/computation/csx_alt.ma".
 
 (* "BIG TREE" STRONGLY NORMALIZING TERMS ************************************)
 
@@ -30,19 +30,18 @@ interpretation
 
 (* Basic eliminators ********************************************************)
 
-theorem fsb_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⦄ →
-                           (⦃G1, L1, T1⦄ ⋕ ⦃G2, L2, T2⦄ → ⊥) → R G2 L2 T2
-                        ) → R G1 L1 T1
-                     ) →
-                     ∀G,L,T. ⦃G, L⦄ ⊢ ⦥[h, g] T → R G L T.
+lemma fsb_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
-/5 width=1 by fpb_fpbc, fsb_intro/
+/4 width=1 by fsb_intro/
 qed-.
 
 (* Basic inversion lemmas ***************************************************)
 
 lemma fsb_inv_csx: ∀h,g,G,L,T. ⦃G, L⦄ ⊢ ⦥[h, g] T → ⦃G, L⦄ ⊢ ⬊*[h, g] T.
-#h #g #G #L #T #H elim H -G -L -T /5 width=1 by csx_intro, fpbc_cpx/
+#h #g #G #L #T #H elim H -G -L -T /5 width=1 by csx_intro_cprs, fpbu_cpxs/
 qed-.