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

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   4 (*      ||A||       A project by Andrea Asperti                           *)
   5 (*      ||T||                                                             *)
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  10 (*       \ /        This file is distributed under the terms of the       *)
  11 (*        v         GNU General Public License Version 2                  *)
  12 (*                                                                        *)
  13 (**************************************************************************)
  14
  15 include "basic_2/relocation/drops_weight.ma".
  16 include "basic_2/s_computation/fqus_weight.ma".
  17 include "basic_2/static/frees.ma".
  18
  19 (* CONTEXT-SENSITIVE FREE VARIABLES *****************************************)
  20
  21 (* Properties with star-iterated supclosure *********************************)
  22
  23 lemma frees_fqus_drops: ∀f1,G,L1,T1. L1 ⊢ 𝐅*⦃T1⦄ ≡ f1 →
  24                         ∀L2,T2. ⦃G, L1, T1⦄ ⊐* ⦃G, L2, T2⦄ →
  25                         ∀I,n. ⬇*[n] L1 ≡ L2.ⓑ{I}T2 →
  26                         ∃∃f2. L2 ⊢ 𝐅*⦃T2⦄ ≡ f2 & f2 ⊆ ⫱*[⫯n] f1.
  27 #f1 #G #L1 #T1 #H elim H -f1 -L1 -T1
  28 [ #f1 #J #Hf1 #L2 #T2 #H12 #I #n #HL12
  29   elim (fqus_inv_atom1 … H12) -H12 #H1 #H2 #H3 destruct
  30   lapply (drops_fwd_lw … HL12) -HL12 #HL12
  31   elim (lt_le_false … HL12) -HL12 //
  32 | #f1 #J #L1 #V1 #s #Hf1 #IH #L2 #T2 #H12
  33   elim (fqus_inv_sort1 … H12) -H12 [ * | #H12 #I * ]
  34   [ -IH -Hf1 #H1 #H2 #H3 #I #n #HL12 destruct
  35     lapply (drops_fwd_lw … HL12) -HL12 #HL12
  36     elim (lt_le_false … HL12) -HL12 //
  37   | -IH #HL12 lapply (drops_fwd_isid … HL12 ?) -HL12 //
  38     #H destruct <(fqus_inv_refl_atom3 … H12) -H12 /2 width=3 by sle_refl, ex2_intro/
  39   | -Hf1 #I #HL12 lapply (drops_inv_drop1 … HL12) -HL12
  40     #HL12 elim (IH … H12 … HL12) -IH -H12 -HL12 /3 width=3 by ex2_intro/
  41   ]
  42 | #f1 #J #L1 #V1 #Hf1 #IH #L2 #T2 #H12
  43   elim (fqus_inv_zero1 … H12) -H12 [ * | #H12 #I * ]
  44   [ -IH -Hf1 #H1 #H2 #H3 #I #n #HL12 destruct
  45     lapply (drops_fwd_lw … HL12) -HL12 #HL12
  46     elim (lt_le_false … HL12) -HL12 //
  47   | -IH -H12 #HL12 lapply (drops_fwd_isid … HL12 ?) -HL12 //
  48      #H destruct /3 width=3 by sle_refl, ex2_intro/
  49   | -Hf1 #n #HL12 lapply (drops_inv_drop1 … HL12) -HL12
  50     #HL12 elim (IH … H12 … HL12) -IH -H12 -HL12 /3 width=3 by ex2_intro/
  51   ]
  52 | #f1 #J #L1 #V1 #i #Hf1 #IH #L2 #T2 #H12
  53   elim (fqus_inv_lref1 … H12) -H12 [ * | #H12 #I * ]
  54   [ -IH -Hf1 #H1 #H2 #H3 #I #n #HL12 destruct
  55     lapply (drops_fwd_lw … HL12) -HL12 #HL12
  56     elim (lt_le_false … HL12) -HL12 //
  57   | -IH #HL12 lapply (drops_fwd_isid … HL12 ?) -HL12 //
  58     #H destruct <(fqus_inv_refl_atom3 … H12) -H12 /2 width=3 by sle_refl, ex2_intro/
  59   | -Hf1 #I #HL12 lapply (drops_inv_drop1 … HL12) -HL12
  60     #HL12 elim (IH … H12 … HL12) -IH -H12 -HL12 /3 width=3 by ex2_intro/
  61   ]
  62 | #f1 #J #L1 #V1 #l #Hf1 #IH #L2 #T2 #H12
  63   elim (fqus_inv_gref1 … H12) -H12 [ * | #H12 #I * ]
  64   [ -IH -Hf1 #H1 #H2 #H3 #I #n #HL12 destruct
  65     lapply (drops_fwd_lw … HL12) -HL12 #HL12
  66     elim (lt_le_false … HL12) -HL12 //
  67   | -IH #HL12 lapply (drops_fwd_isid … HL12 ?) -HL12 //
  68     #H destruct <(fqus_inv_refl_atom3 … H12) -H12 /2 width=3 by sle_refl, ex2_intro/
  69   | -Hf1 #I #HL12 lapply (drops_inv_drop1 … HL12) -HL12
  70     #HL12 elim (IH … H12 … HL12) -IH -H12 -HL12 /3 width=3 by ex2_intro/
  71   ]
  72 | #f1V #f1T #f1 #p #J #L1 #V #T #_ #_ #Hf1 #IHV #IHT #L2 #T2 #H12 #I #n #HL12
  73   elim (fqus_inv_bind1 … H12) -H12 [ * |*: #H12 ]
  74   [ -IHV -IHT -Hf1 #H1 #H2 #H3 destruct
  75     lapply (drops_fwd_lw … HL12) -HL12 #HL12
  76     elim (lt_le_false … HL12) -HL12 //
  77   | -IHT elim (IHV … H12 … HL12) -IHV -H12 -HL12
  78     /4 width=6 by sor_tls, sor_sle_sn, ex2_intro/
  79   | -IHV elim (IHT … H12 I (⫯n)) -IHT -H12 /2 width=1 by drops_drop/ -HL12
  80     <tls_xn /4 width=6 by ex2_intro, sor_tls, sor_sle_dx/
  81   ]
  82 | #f1V #f1T #f1 #J #L1 #V #T #_ #_ #Hf1 #IHV #IHT #L2 #T2 #H12 #I #n #HL12
  83   elim (fqus_inv_flat1 … H12) -H12 [ * |*: #H12 ]
  84   [ -IHV -IHT -Hf1 #H1 #H2 #H3 destruct
  85     lapply (drops_fwd_lw … HL12) -HL12 #HL12
  86     elim (lt_le_false … HL12) -HL12 //
  87   | -IHT elim (IHV … H12 … HL12) -IHV -H12 -HL12
  88     /4 width=6 by sor_tls, sor_sle_sn, ex2_intro/
  89   | -IHV elim (IHT … H12 … HL12) -IHT -H12 -HL12
  90     /4 width=6 by ex2_intro, sor_tls, sor_sle_dx/
  91   ]
  92 ]
  93 qed-.