matita/matita/contribs/lambdadelta/basic_2/etc_2A1/sta/lstas_lstas.etc

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  14
  15 include "basic_2/static/sta_sta.ma".
  16 include "basic_2/unfold/lstas_lift.ma".
  17
  18 (* NAT-ITERATED STATIC TYPE ASSIGNMENT FOR TERMS ****************************)
  19
  20 (* Main properties **********************************************************)
  21
  22 theorem lstas_trans: ∀h,G,L. ltransitive … (lstas h G L).
  23 /2 width=3 by lstar_ltransitive/ qed-.
  24
  25 theorem lstas_mono: ∀h,G,L,l. singlevalued … (lstas h G L l).
  26 /3 width=7 by sta_mono, lstar_singlevalued/ qed-.
  27
  28 theorem lstas_conf_le: ∀h,G,L,T,U1,l1. ⦃G, L⦄ ⊢ T •*[h, l1] U1 →
  29                        ∀U2,l2. l1 ≤ l2 → ⦃G, L⦄ ⊢ T •*[h, l2] U2 →
  30                        ⦃G, L⦄ ⊢ U1 •*[h, l2-l1] U2.
  31 #h #G #L #T #U1 #l1 #HTU1 #U2 #l2 #Hl12
  32 >(plus_minus_m_m … Hl12) in ⊢ (%→?); -Hl12 >commutative_plus #H
  33 elim (lstas_split … H) -H #U #HTU
  34 >(lstas_mono … HTU … HTU1) -T //
  35 qed-.
  36
  37 (* Advanced properties ******************************************************)
  38
  39 lemma lstas_sta_conf_pos: ∀h,G,L,T,U1. ⦃G, L⦄ ⊢ T •[h] U1 →
  40                           ∀U2,l. ⦃G, L⦄ ⊢ T •*[h, l+1] U2 → ⦃G, L⦄ ⊢ U1 •*[h, l] U2.
  41 #h #G #L #T #U1 #HTU1 #U2 #l #HTU2
  42 lapply (lstas_conf_le … T U1 1 … HTU2) -HTU2 /2 width=1 by sta_lstas/
  43 qed-.
  44
  45 lemma lstas_strip_pos: ∀h,G,L,T1,U1. ⦃G, L⦄ ⊢ T1 •[h] U1 →
  46                        ∀T2,l. ⦃G, L⦄ ⊢ T1 •*[h, l+1] T2 →
  47                        ∃∃U2. ⦃G, L⦄ ⊢ T2 •[h] U2 & ⦃G, L⦄ ⊢ U1 •*[h, l+1] U2.
  48 #h #G #L #T1 #U1 #HTU1 #T2 #l #HT12
  49 elim (lstas_fwd_correct … HTU1 … HT12)
  50 lapply (lstas_sta_conf_pos … HTU1 … HT12) -T1 /3 width=5 by lstas_step_dx, ex2_intro/
  51 qed-.