matita/matita/contribs/lambdadelta/basic_2/etc/ssta1/lsstas_lsstas.etc

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