matita/matita/contribs/lambdadelta/basic_2/etc/fid/fle_fid.etc

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  14
  15 include "basic_2/static/fid.ma".
  16 include "basic_2/static/fle_fqup.ma".
  17
  18 (* FREE VARIABLES INCLUSION FOR RESTRICTED CLOSURES *************************)
  19
  20 (* Properties with free variables identity for restricted closures **********)
  21
  22 lemma fle_fid_sn: ∀L1,L2. |L1| = |L2| →
  23                   ∀T1,T2. 𝐈⦃L1, T1⦄ → ⦃L1, T1⦄ ⊆ ⦃L2, T2⦄.
  24 #L1 #L2 #HL #T1 #T2 #HT1
  25 elim (frees_total L1 T1) #f1 #Hf1
  26 elim (frees_total L2 T2) #f2 #Hf2
  27 /4 width=8 by lveq_length_eq, sle_isid_sn, ex4_4_intro/
  28 qed.
  29
  30 (* Inversion lemmas with free variables identity for restricted closures ****)
  31
  32 lemma fle_inv_fid_dx: ∀L1,L2. |L1| = |L2| →
  33                       ∀T1,T2. ⦃L1, T1⦄ ⊆ ⦃L2, T2⦄ →  𝐈⦃L2, T2⦄ → 𝐈⦃L1, T1⦄.
  34 #L1 #L2 #HL #T1 #T2
  35 * #n1 #n2 #f1 #f2 #Hf1 #Hf2 #HL12 #Hf12 #HT2 #g1 #Hg1
  36 elim (lveq_inj_length … HL12) // -HL -HL12 #H1 #H2 destruct
  37 lapply (frees_mono … Hf1 … Hg1) -Hg1 #Hfg1
  38 /4 width=5 by sle_inv_isid_dx, isid_eq_repl_back/
  39 qed-.