matita/matita/contribs/lambdadelta/basic_2A/etc/sta/lstas_da.etc

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  14
  15 include "basic_2/unfold/lstas.ma".
  16 include "basic_2/static/da_sta.ma".
  17
  18 (* NAT-ITERATED STATIC TYPE ASSIGNMENT FOR TERMS ****************************)
  19
  20 (* Properties on degree assignment for terms ********************************)
  21
  22 lemma lstas_da_conf: ∀h,g,G,L,T,U,l1. ⦃G, L⦄ ⊢ T •*[h, l1] U →
  23                      ∀l2. ⦃G, L⦄ ⊢ T ▪[h, g] l2 → ⦃G, L⦄ ⊢ U ▪[h, g] l2-l1.
  24 #h #g #G #L #T #U #l1 #H @(lstas_ind_dx … H) -U -l1 //
  25 #l1 #U #U0 #_ #HU0 #IHTU #l2 #HT
  26 <minus_plus /3 width=3 by da_sta_conf/
  27 qed-.
  28
  29 (* Advanced inversion lemmas ************************************************)
  30
  31 lemma lstas_inv_refl_pos: ∀h,G,L,T,l. ⦃G, L⦄ ⊢ T •*[h, l+1] T → ⊥.
  32 #h #G #L #T #l #H elim (lstas_inv_step_sn … H)
  33 #U #HTU #_ elim (sta_da_ge … (l+1) HTU) -U
  34 #g #l0 #HT #Hl0 lapply (lstas_da_conf … H … HT) -H
  35 #H0T lapply (da_mono … HT … H0T) -h -G -L -T
  36 #H elim (discr_x_minus_xy … H) -H
  37 [ #H destruct /2 width=3 by le_plus_xSy_O_false/
  38 | -Hl0 <plus_n_Sm #H destruct
  39 ]
  40 qed-.