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4 (* ||A|| A project by Andrea Asperti *)
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7 (* ||T|| The HELM team. *)
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15 include "basic_2/notation/relations/predsn_8.ma".
16 include "basic_2/grammar/bteq.ma".
17 include "basic_2/reduction/lpx.ma".
19 (* ADJACENT "BIG TREE" NORMAL FORMS *****************************************)
21 definition fpn: ∀h. sd h → tri_relation genv lenv term ≝
22 λh,g,G1,L1,T1,G2,L2,T2.
23 ∧∧ G1 = G2 & ⦃G1, L1⦄ ⊢ ➡[h, g] L2 & T1 = T2.
26 "adjacent 'big tree' normal forms (closure)"
27 'PRedSn h g G1 L1 T1 G2 L2 T2 = (fpn h g G1 L1 T1 G2 L2 T2).
29 (* Basic_properties *********************************************************)
31 lemma fpn_refl: ∀h,g. tri_reflexive … (fpn h g).
32 /2 width=1 by and3_intro/ qed.
34 (* Basic forward lemmas *****************************************************)
36 lemma fpn_fwd_bteq: ∀h,g,G1,G2,L1,L2,T1,T2. ⦃G1, L1, T1⦄ ⊢➡[h, g] ⦃G2, L2, T2⦄ →
37 ⦃G1, L1, T1⦄ ⋕ ⦃G2, L2, T2⦄.
38 #h #g #G1 #G2 #L1 #L2 #T1 #T2 * /3 width=4 by lpx_fwd_length, and3_intro/