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

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  14
  15 include "basic_2/static/lsubf.ma".
  16
  17 (* RESTRICTED REFINEMENT FOR CONTEXT-SENSITIVE FREE VARIABLES ***************)
  18
  19 (* Properties with context-sensitive free variables *************************)
  20
  21 lemma lsubf_free_trans: ∀f2,L2,T. L2 ⊢ 𝐅*⦃T⦄ ≡ f2 → ∀f,L1. ⦃L1, f⦄ ⫃𝐅* ⦃L2, f2⦄ →
  22                         ∃∃f1. L1 ⊢ 𝐅*⦃T⦄ ≡ f1 & f1 ⊆ f.
  23 #f2 #L2 #T #H elim H -f2 -L2 -T
  24 [ #f2 #I #Hf2 #f #L1 #H elim (lsubf_inv_atom2 … H) -H
  25   #H1 #H2 destruct /3 width=3 by frees_atom, sle_refl, ex2_intro/
  26 | #f2 #I #K2 #W #s #_ #IH #f #L1 #H elim (lsubf_inv_push2 … H) -H *
  27   [ #g1 #K1 #H12 #H1 #H2
  28   | #g #g1 #K1 #V #Hg #Hg1 #H12 #H1 #H2 #H3
  29   ] destruct elim (IH … H12) -f2 -K2
  30   /3 width=7 by frees_sort, sle_push, ex2_intro/
  31 | #f2 #I #K2 #W #_ #IH #f #L1 #H elim (lsubf_inv_next2 … H) -H *
  32   [ #g1 #K1 #H12 #H1 #H2 destruct elim (IH … H12) -f2 -K2
  33     /3 width=7 by frees_zero, sle_next, ex2_intro/
  34   | #g #g1 #K1 #V #Hg #Hg1 #H12 #H1 #H2 #H3 destruct
  35     elim (IH … H12) -K2 #f1 #Hf1 #Hfg1
  36     elim (sor_isfin_ex … f1 g ??)
  37     /5 width=10 by frees_fwd_isfin, frees_flat, frees_zero, monotonic_sle_sor, sor_inv_sle_dx, sor_sle_sn, sle_next, ex2_intro/
  38   ]
  39 | #f2 #I #K2 #W #i #_ #IH #f #L1 #H elim (lsubf_inv_push2 … H) -H *
  40   [ #g1 #K1 #H12 #H1 #H2
  41   | #g #g1 #K1 #V #Hg #Hg1 #H12 #H1 #H2 #H3
  42   ] destruct elim (IH … H12) -f2 -K2
  43   /3 width=7 by frees_lref, sle_push, ex2_intro/
  44 | #f2 #I #K2 #W #l #_ #IH #f #L1 #H elim (lsubf_inv_push2 … H) -H *
  45   [ #g1 #K1 #H12 #H1 #H2
  46   | #g #g1 #K1 #V #Hg #Hg1 #H12 #H1 #H2 #H3
  47   ] destruct elim (IH … H12) -f2 -K2
  48   /3 width=7 by frees_gref, sle_push, ex2_intro/
  49 | #f2V #f2T #f2 #p #I #L2 #V #T #_ #_ #Hf2 #IHV #IHT #f #L1 #H12
  50 | #f2V #f2T #f2 #I #L2 #V #T #_ #_ #Hf2 #IHV #IHT #f #L1 #H12
  51