+++ /dev/null
-(**************************************************************************)
-(* ___ *)
-(* ||M|| *)
-(* ||A|| A project by Andrea Asperti *)
-(* ||T|| *)
-(* ||I|| Developers: *)
-(* ||T|| The HELM team. *)
-(* ||A|| http://helm.cs.unibo.it *)
-(* \ / *)
-(* \ / This file is distributed under the terms of the *)
-(* v GNU General Public License Version 2 *)
-(* *)
-(**************************************************************************)
-
-include "basic_2/notation/relations/btpredsnstar_8.ma".
-include "basic_2/reduction/fpn.ma".
-
-(* COMPUTATION FOR "BIG TREE" NORMAL FORMS **********************************)
-
-definition fpns: ∀h. sd h → tri_relation genv lenv term ≝
- λh,g. tri_TC … (fpn h g).
-
-interpretation
- "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 eliminators ********************************************************)
-
-lemma fpns_ind: ∀h,g,G1,L1,T1. ∀R:relation3 …. R G1 L1 T1 →
- (∀G,G2,L,L2,T,T2. ⦃G1, L1, T1⦄ ⊢ ⋕➡*[h, g] ⦃G, L, T⦄ → ⦃G, L, T⦄ ⊢ ⋕➡[h, g] ⦃G2, L2, T2⦄ → R G L T → R G2 L2 T2) →
- ∀G2,L2,T2. ⦃G1, L1, T1⦄ ⊢ ⋕➡*[h, g] ⦃G2, L2, T2⦄ → R G2 L2 T2.
-#h #g #G1 #L1 #T1 #R #IH1 #IH2 #G2 #L2 #T2 #H
-lapply (tri_TC_star_ind … IH1 IH2 G2 L2 T2 H) //
-qed-.
-
-lemma fpns_ind_dx: ∀h,g,G2,L2,T2. ∀R:relation3 …. R G2 L2 T2 →
- (∀G1,G,L1,L,T1,T. ⦃G1, L1, T1⦄ ⊢ ⋕➡[h, g] ⦃G, L, T⦄ → ⦃G, L, T⦄ ⊢ ⋕➡*[h, g] ⦃G2, L2, T2⦄ → R G L T → R G1 L1 T1) →
- ∀G1,L1,T1. ⦃G1, L1, T1⦄ ⊢ ⋕➡*[h, g] ⦃G2, L2, T2⦄ → R G1 L1 T1.
-#h #g #G2 #L2 #T2 #R #IH1 #IH2 #G1 #L1 #T1 #H
-@(tri_TC_star_ind_dx … IH1 IH2 G1 L1 T1 H) //
-qed-.
-
-(* Basic_properties *********************************************************)
-
-lemma fpns_refl: ∀h,g. tri_reflexive … (fpns h g).
-/2 width=1 by tri_inj/ 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⦄.
-/2 width=1 by tri_inj/ qed.
-
-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⦄.
-/2 width=5 by tri_step/ 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⦄.
-/2 width=5 by tri_TC_strap/ qed-.