matita/matita/contribs/lambdadelta/basic_2A/substitution/gget_gget.ma

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  14
  15 include "basic_2A/substitution/gget.ma".
  16
  17 (* GLOBAL ENVIRONMENT READING ***********************************************)
  18
  19 (* Main properties **********************************************************)
  20
  21 theorem gget_mono: ∀G,G1,m. ⬇[m] G ≡ G1 → ∀G2. ⬇[m] G ≡ G2 → G1 = G2.
  22 #G #G1 #m #H elim H -G -G1
  23 [ #G #Hm #G2 #H
  24   >(gget_inv_gt … H Hm) -H -Hm //
  25 | #G #Hm #G2 #H
  26   >(gget_inv_eq … H Hm) -H -Hm //
  27 | #I #G #G1 #V #Hm #_ #IHG1 #G2 #H
  28   lapply (gget_inv_lt … H Hm) -H -Hm /2 width=1 by/
  29 ]
  30 qed-.
  31
  32 lemma gget_dec: ∀G1,G2,m. Decidable (⬇[m] G1 ≡ G2).
  33 #G1 #G2 #m
  34 elim (gget_total m G1) #G #HG1
  35 elim (eq_genv_dec G G2) #HG2
  36 [ destruct /2 width=1 by or_introl/
  37 | @or_intror #HG12
  38   lapply (gget_mono … HG1 … HG12) -HG1 -HG12 /2 width=1 by/
  39 ]
  40 qed-.