matita/matita/contribs/lambdadelta/basic_2/unfold/sstas_sstas.ma

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  14
  15 include "basic_2/static/ssta_ssta.ma".
  16 include "basic_2/unfold/sstas.ma".
  17
  18 (* ITERATED STRATIFIED STATIC TYPE ASSIGNMENT FOR TERMS *********************)
  19
  20 (* Advanced inversion lemmas ************************************************)
  21
  22 lemma sstas_inv_O: ∀h,g,L,T,U. ⦃h, L⦄ ⊢ T •*[g] U →
  23                    ∀T0. ⦃h, L⦄ ⊢ T •[g] ⦃0, T0⦄ → U = T.
  24 #h #g #L #T #U #H @(sstas_ind_dx … H) -T //
  25 #T0 #U0 #l0 #HTU0 #_ #_ #T1 #HT01
  26 elim (ssta_mono … HTU0 … HT01) <plus_n_Sm #H destruct
  27 qed-.
  28
  29 (* Advanced properties ******************************************************)
  30
  31 lemma sstas_strip: ∀h,g,L,T,U1. ⦃h, L⦄ ⊢ T •*[g] U1 →
  32                    ∀U2,l. ⦃h, L⦄ ⊢ T •[g] ⦃l, U2⦄ →
  33                    T = U1 ∨ ⦃h, L⦄ ⊢ U2 •*[g] U1.
  34 #h #g #L #T #U1 #H1 @(sstas_ind_dx … H1) -T /2 width=1/
  35 #T #U #l0 #HTU #HU1 #_ #U2 #l #H2
  36 elim (ssta_mono … H2 … HTU) -H2 -HTU #H1 #H2 destruct /2 width=1/
  37 qed-.
  38
  39 (* Main properties **********************************************************)
  40
  41 theorem sstas_trans: ∀h,g,L,T1,U. ⦃h, L⦄ ⊢ T1 •*[g] U →
  42                      ∀T2. ⦃h, L⦄ ⊢ U •*[g] T2 → ⦃h, L⦄ ⊢ T1 •*[g] T2.
  43 /2 width=3/ qed-.
  44
  45 theorem sstas_conf: ∀h,g,L,T,U1. ⦃h, L⦄ ⊢ T •*[g] U1 →
  46                     ∀U2. ⦃h, L⦄ ⊢ T •*[g] U2 →
  47                    ⦃h, L⦄ ⊢ U1 •*[g] U2 ∨ ⦃h, L⦄ ⊢ U2 •*[g] U1.
  48 #h #g #L #T #U1 #H1 @(sstas_ind_dx … H1) -T /2 width=1/
  49 #T #U #l #HTU #HU1 #IHU1 #U2 #H2
  50 elim (sstas_strip … H2 … HTU) #H destruct
  51 [ -H2 -IHU1 /3 width=4/
  52 | -T /2 width=1/
  53 ]
  54 qed-.