matita/matita/contribs/lambdadelta/basic_2/static/fsle_length.ma

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  11 (*        v         GNU General Public License Version 2                  *)
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  14
  15 include "basic_2/syntax/lveq_length.ma".
  16 include "basic_2/static/fsle.ma".
  17
  18 (* FREE VARIABLES INCLUSION FOR RESTRICTED CLOSURES *************************)
  19
  20 (* Properties with length for local environments ****************************)
  21
  22 lemma fsle_sort_bi: ∀L1,L2,s1,s2. |L1| = |L2| → ⦃L1, ⋆s1⦄ ⊆ ⦃L2, ⋆s2⦄.
  23 /3 width=8 by lveq_length_eq, frees_sort, sle_refl, ex4_4_intro/ qed.
  24
  25 lemma fsle_gref_bi: ∀L1,L2,l1,l2. |L1| = |L2| → ⦃L1, §l1⦄ ⊆ ⦃L2, §l2⦄.
  26 /3 width=8 by lveq_length_eq, frees_gref, sle_refl, ex4_4_intro/ qed.
  27
  28 lemma fsle_pair_bi: ∀K1,K2. |K1| = |K2| → ∀V1,V2. ⦃K1, V1⦄ ⊆ ⦃K2, V2⦄ →
  29                     ∀I1,I2. ⦃K1.ⓑ{I1}V1, #O⦄ ⊆ ⦃K2.ⓑ{I2}V2, #O⦄.
  30 #K1 #K2 #HK #V1 #V2
  31 * #n1 #n2 #f1 #f2 #Hf1 #Hf2 #HK12 #Hf12
  32 #I1 #I2
  33 elim (lveq_inj_length … HK12) // -HK #H1 #H2 destruct
  34 /3 width=12 by frees_pair, lveq_bind, sle_next, ex4_4_intro/
  35 qed.
  36
  37 lemma fsle_unit_bi: ∀K1,K2. |K1| = |K2| →
  38                     ∀I1,I2. ⦃K1.ⓤ{I1}, #O⦄ ⊆ ⦃K2.ⓤ{I2}, #O⦄.
  39 /3 width=8 by frees_unit, lveq_length_eq, sle_refl, ex4_4_intro/
  40 qed.