matita/matita/contribs/lambdadelta/basic_2/computation/fpns.ma

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  14
  15 include "basic_2/notation/relations/predsnstar_8.ma".
  16 include "basic_2/reduction/fpn.ma".
  17 include "basic_2/computation/lpxs.ma".
  18
  19 (* ORDERED "BIG TREE" NORMAL FORMS ******************************************)
  20
  21 definition fpns: ∀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.
  24
  25 interpretation
  26    "ordered 'big tree' normal forms (closure)"
  27    'PRedSnStar h g G1 L1 T1 G2 L2 T2 = (fpns h g G1 L1 T1 G2 L2 T2).
  28
  29 (* Basic_properties *********************************************************)
  30
  31 lemma fpns_refl: ∀h,g. tri_reflexive … (fpns h g).
  32 /2 width=1 by and3_intro/ qed.
  33
  34 lemma fpn_fpns: ∀h,g,G1,G2,L1,L2,T1,T2. ⦃G1, L1, T1⦄ ⊢ ➡[h, g] ⦃G2, L2, T2⦄ →
  35                 ⦃G1, L1, T1⦄ ⊢ ➡*[h, g] ⦃G2, L2, T2⦄.
  36 #h #g #G1 #G2 #L1 #L2 #T1 #T2 * /3 width=1 by lpx_lpxs, and3_intro/
  37 qed.
  38
  39 lemma fpns_strap1: ∀h,g,G1,G,G2,L1,L,L2,T1,T,T2. ⦃G1, L1, T1⦄ ⊢ ➡*[h, g] ⦃G, L, T⦄ →
  40                    ⦃G, L, T⦄ ⊢ ➡[h, g] ⦃G2, L2, T2⦄ → ⦃G1, L1, T1⦄ ⊢ ➡*[h, g] ⦃G2, L2, T2⦄.
  41 #h #g #G1 #G #G2 #L1 #L #L2 #T1 #T #T2 * #H1G #H1L #G1T *
  42 /3 width=3 by lpxs_strap1, and3_intro/
  43 qed-.
  44
  45 lemma fpns_strap2: ∀h,g,G1,G,G2,L1,L,L2,T1,T,T2. ⦃G1, L1, T1⦄ ⊢ ➡[h, g] ⦃G, L, T⦄ →
  46                    ⦃G, L, T⦄ ⊢ ➡*[h, g] ⦃G2, L2, T2⦄ → ⦃G1, L1, T1⦄ ⊢ ➡*[h, g] ⦃G2, L2, T2⦄.
  47 #h #g #G1 #G #G2 #L1 #L #L2 #T1 #T #T2 * #H1G #H1L #G1T *
  48 /3 width=3 by lpxs_strap2, and3_intro/
  49 qed-.
  50
  51 (* Basic forward lemmas *****************************************************)
  52
  53 lemma fpns_fwd_bteq: ∀h,g,G1,G2,L1,L2,T1,T2. ⦃G1, L1, T1⦄ ⊢ ➡*[h, g] ⦃G2, L2, T2⦄ →
  54                      ⦃G1, L1, T1⦄ ⋕ ⦃G2, L2, T2⦄.
  55 #h #g #G1 #G2 #L1 #L2 #T1 #T2 * /3 width=4 by lpxs_fwd_length, and3_intro/
  56 qed-.