second and third commutation property on lazy equivalence for

[helm.git] / matita / matita / contribs / lambdadelta / basic_2 / etc / fpn / fpn.etc

diff --git a/matita/matita/contribs/lambdadelta/basic_2/etc/fpn/fpn.etc b/matita/matita/contribs/lambdadelta/basic_2/etc/fpn/fpn.etc
index f33adbde94f4ab7280f079d6ba7947f161df80ed..406e6eb8e67a0954ab39cf008803b7ba2c74e7d9 100644 (file)
--- a/matita/matita/contribs/lambdadelta/basic_2/etc/fpn/fpn.etc
+++ b/matita/matita/contribs/lambdadelta/basic_2/etc/fpn/fpn.etc
@@ -12,28 +12,28 @@
 (*                                                                        *)
 (**************************************************************************)
 
-include "basic_2/notation/relations/predsn_8.ma".
-include "basic_2/grammar/bteq.ma".
+include "basic_2/notation/relations/btpredsn_8.ma".
+include "basic_2/relocation/lleq.ma".
 include "basic_2/reduction/lpx.ma".
 
-(* ADJACENT "BIG TREE" NORMAL FORMS *****************************************)
+(* REDUCTION FOR "BIG TREE" NORMAL FORMS ************************************)
 
-definition fpn: ∀h. sd h → tri_relation genv lenv term ≝
-                λh,g,G1,L1,T1,G2,L2,T2.
-                ∧∧ G1 = G2 & ⦃G1, L1⦄ ⊢ ➡[h, g] L2 & T1 = T2.
+inductive fpn (h) (g) (G) (L1) (T): relation3 genv lenv term ≝
+| fpn_intro: ∀L2. ⦃G, L1⦄ ⊢ ➡[h, g] L2 → L1 ⋕[T] L2 → fpn h g G L1 T G L2 T
+.
 
 interpretation
-   "adjacent 'big tree' normal forms (closure)"
-   'PRedSn h g G1 L1 T1 G2 L2 T2 = (fpn h g G1 L1 T1 G2 L2 T2).
+   "reduction for 'big tree' normal forms (closure)"
+   'BTPRedSn h g G1 L1 T1 G2 L2 T2 = (fpn h g G1 L1 T1 G2 L2 T2).
 
 (* Basic_properties *********************************************************)
 
 lemma fpn_refl: ∀h,g. tri_reflexive … (fpn h g).
-/2 width=1 by and3_intro/ qed.
+/2 width=1 by fpn_intro/ qed.
 
-(* Basic forward lemmas *****************************************************)
+(* Basic inversion lemmas ***************************************************) 
 
-lemma fpn_fwd_bteq: ∀h,g,G1,G2,L1,L2,T1,T2. ⦃G1, L1, T1⦄ ⊢➡[h, g] ⦃G2, L2, T2⦄ →
-                    ⦃G1, L1, T1⦄ ⋕ ⦃G2, L2, T2⦄.
-#h #g #G1 #G2 #L1 #L2 #T1 #T2 * /3 width=4 by lpx_fwd_length, and3_intro/
+lemma fpn_inv_gen: ∀h,g,G1,G2,L1,L2,T1,T2. ⦃G1, L1, T1⦄ ⊢ ⋕➡[h, g] ⦃G2, L2, T2⦄ →
+                   ∧∧ G1 = G2 & ⦃G1, L1⦄ ⊢ ➡[h, g] L2 & L1 ⋕[T1] L2 & T1 = T2.
+#h #g #G1 #G2 #L1 #L2 #T1 #T2 * -G2 -L2 -T2 /2 width=1 by and4_intro/
 qed-.