matita/matita/contribs/lambdadelta/basic_2/rt_transition/fpbq_fpb.ma

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  14
  15 include "basic_2/rt_transition/fpb_fdeq.ma".
  16 include "basic_2/rt_transition/fpbq.ma".
  17
  18 (* PARALLEL RST-TRANSITION FOR CLOSURES *************************************)
  19
  20 (* Properties with proper parallel rst-transition for closures **************)
  21
  22 lemma fpb_fpbq: ∀h,G1,G2,L1,L2,T1,T2. ⦃G1, L1, T1⦄ ≻[h] ⦃G2, L2, T2⦄ →
  23                 ⦃G1, L1, T1⦄ ≽[h] ⦃G2, L2, T2⦄.
  24 #h #G1 #G2 #L1 #L2 #T1 #T2 * -G2 -L2 -T2
  25 /3 width=1 by fpbq_fquq, fpbq_cpx, fpbq_lpx, fqu_fquq/
  26 qed.
  27
  28 (* Basic_2A1: fpb_fpbq_alt *)
  29 lemma fpb_fpbq_ffdneq: ∀h,G1,G2,L1,L2,T1,T2. ⦃G1, L1, T1⦄ ≻[h] ⦃G2, L2, T2⦄ →
  30                        ∧∧ ⦃G1, L1, T1⦄ ≽[h] ⦃G2, L2, T2⦄ & (⦃G1, L1, T1⦄ ≛ ⦃G2, L2, T2⦄ → ⊥).
  31 /3 width=10 by fpb_fpbq, fpb_inv_fdeq, conj/ qed-.
  32
  33 (* Inversrion lemmas with proper parallel rst-transition for closures *******)
  34
  35 (* Basic_2A1: uses: fpbq_ind_alt *)
  36 lemma fpbq_inv_fpb: ∀h,G1,G2,L1,L2,T1,T2. ⦃G1, L1, T1⦄ ≽[h] ⦃G2, L2, T2⦄ →
  37                     ∨∨ ⦃G1, L1, T1⦄ ≛ ⦃G2, L2, T2⦄
  38                      | ⦃G1, L1, T1⦄ ≻[h] ⦃G2, L2, T2⦄.
  39 #h #G1 #G2 #L1 #L2 #T1 #T2 * -G2 -L2 -T2
  40 [ #G2 #L2 #T2 * [2: * #H1 #H2 #H3 destruct ]
  41   /3 width=1 by fpb_fqu, fdeq_intro_sn, or_intror, or_introl/
  42 | #T2 #H elim (tdeq_dec T1 T2)
  43   /4 width=1 by fpb_cpx, fdeq_intro_sn, or_intror, or_introl/
  44 | #L2 elim (rdeq_dec L1 L2 T1)
  45   /4 width=1 by fpb_lpx, fdeq_intro_sn, or_intror, or_introl/
  46 | /2 width=1 by or_introl/
  47 ]
  48 qed-.
  49
  50 (* Basic_2A1: fpbq_inv_fpb_alt *)
  51 lemma fpbq_ffdneq_inv_fpb: ∀h,G1,G2,L1,L2,T1,T2. ⦃G1, L1, T1⦄ ≽[h] ⦃G2, L2, T2⦄ →
  52                            (⦃G1, L1, T1⦄ ≛ ⦃G2, L2, T2⦄ → ⊥) → ⦃G1, L1, T1⦄ ≻[h] ⦃G2, L2, T2⦄.
  53 #h #G1 #G2 #L1 #L2 #T1 #T2 #H #H0
  54 elim (fpbq_inv_fpb … H) -H // #H elim H0 -H0 //
  55 qed-.