theory of cpy is complete!

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

diff --git a/matita/matita/contribs/lambdadelta/basic_2/computation/fpns.ma b/matita/matita/contribs/lambdadelta/basic_2/computation/fpns.ma
index 29b81d043e8f2abbc2a1a2fec6dd2246b46d39cf..beb022541e83e55ffc3570c1712a212089cdf866 100644 (file)
--- a/matita/matita/contribs/lambdadelta/basic_2/computation/fpns.ma
+++ b/matita/matita/contribs/lambdadelta/basic_2/computation/fpns.ma
@@ -12,45 +12,28 @@
 (*                                                                        *)
 (**************************************************************************)
 
-include "basic_2/notation/relations/predsnstar_8.ma".
-include "basic_2/reduction/fpn.ma".
+include "basic_2/notation/relations/btpredsnstar_8.ma".
+include "basic_2/relocation/lleq.ma".
 include "basic_2/computation/lpxs.ma".
 
-(* ORDERED "BIG TREE" NORMAL FORMS ******************************************)
+(* PARALLEL COMPUTATION FOR "BIG TREE" NORMAL FORMS *************************)
 
-definition fpns: ∀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 fpns (h) (g) (G) (L1) (T): relation3 genv lenv term ≝
+| fpns_intro: ∀L2. ⦃G, L1⦄ ⊢ ➡*[h, g] L2 → L1 ⋕[0, T] L2 → fpns h g G L1 T G L2 T
+.
 
 interpretation
-   "ordered 'big tree' normal forms (closure)"
-   'PRedSnStar h g G1 L1 T1 G2 L2 T2 = (fpns h g G1 L1 T1 G2 L2 T2).
+   "computation for 'big tree' normal forms (closure)"
+   'BTPRedSnStar h g G1 L1 T1 G2 L2 T2 = (fpns h g G1 L1 T1 G2 L2 T2).
 
 (* Basic_properties *********************************************************)
 
 lemma fpns_refl: ∀h,g. tri_reflexive … (fpns h g).
-/2 width=1 by and3_intro/ qed.
+/2 width=1 by fpns_intro/ qed.
 
-lemma fpn_fpns: ∀h,g,G1,G2,L1,L2,T1,T2. ⦃G1, L1, T1⦄ ⊢ ➡[h, g] ⦃G2, L2, T2⦄ →
-                ⦃G1, L1, T1⦄ ⊢ ➡*[h, g] ⦃G2, L2, T2⦄.
-#h #g #G1 #G2 #L1 #L2 #T1 #T2 * /3 width=1 by lpx_lpxs, and3_intro/
-qed.
+(* Basic inversion lemmas ***************************************************) 
 
-lemma fpns_strap1: ∀h,g,G1,G,G2,L1,L,L2,T1,T,T2. ⦃G1, L1, T1⦄ ⊢ ➡*[h, g] ⦃G, L, T⦄ →
-                   ⦃G, L, T⦄ ⊢ ➡[h, g] ⦃G2, L2, T2⦄ → ⦃G1, L1, T1⦄ ⊢ ➡*[h, g] ⦃G2, L2, T2⦄.
-#h #g #G1 #G #G2 #L1 #L #L2 #T1 #T #T2 * #H1G #H1L #G1T *
-/3 width=3 by lpxs_strap1, and3_intro/
-qed-.
-
-lemma fpns_strap2: ∀h,g,G1,G,G2,L1,L,L2,T1,T,T2. ⦃G1, L1, T1⦄ ⊢ ➡[h, g] ⦃G, L, T⦄ →
-                   ⦃G, L, T⦄ ⊢ ➡*[h, g] ⦃G2, L2, T2⦄ → ⦃G1, L1, T1⦄ ⊢ ➡*[h, g] ⦃G2, L2, T2⦄.
-#h #g #G1 #G #G2 #L1 #L #L2 #T1 #T #T2 * #H1G #H1L #G1T *
-/3 width=3 by lpxs_strap2, and3_intro/
-qed-.
-
-(* Basic forward lemmas *****************************************************)
-
-lemma fpns_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 lpxs_fwd_length, and3_intro/
+lemma fpns_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 ⋕[0, T1] L2 & T1 = T2.
+#h #g #G1 #G2 #L1 #L2 #T1 #T2 * -G2 -L2 -T2 /2 width=1 by and4_intro/
 qed-.