matita/matita/contribs/lambdadelta/basic_2/rt_transition/cwhx.ma

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  10 (*       \ /        This file is distributed under the terms of the       *)
  11 (*        v         GNU General Public License Version 2                  *)
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  13 (**************************************************************************)
  14
  15 include "basic_2/notation/relations/predtywhead_4.ma".
  16 include "static_2/syntax/item_sh.ma".
  17 include "static_2/syntax/lenv.ma".
  18 include "static_2/syntax/genv.ma".
  19
  20 (* WHD NORMAL TERMS FOR UNBOUND CONTEXT-SENSITIVE PARALLEL RT-TRANSITION ****)
  21
  22 inductive cwhx (h:sh) (G:genv): relation2 lenv term ≝
  23 | cwhx_sort: ∀L,s. cwhx h G L (⋆s)
  24 | cwhx_abst: ∀p,L,W,T. cwhx h G L (ⓛ{p}W.T)
  25 | cwhx_ldef: ∀L,V,T. cwhx h G (L.ⓓV) T → cwhx h G L (-ⓓV.T)
  26 .
  27
  28 interpretation
  29    "whd normality for unbound context-sensitive parallel rt-transition (term)"
  30    'PRedTyWHead h G L T = (cwhx h G L T).
  31
  32 (* Basic inversion lemmas ***************************************************)
  33
  34 fact cwhx_inv_lref_aux (h) (G):
  35                        ∀Y,X. ⦃G,Y⦄ ⊢ ⬈[h] 𝐖𝐇⦃X⦄ →
  36                        ∀i. X = #i → ⊥.
  37 #h #G #Y #X * - X -Y
  38 [ #L #s #i #H destruct
  39 | #p #L #W #T #i #H destruct
  40 | #L #V #T #_ #i #H destruct
  41 ]
  42 qed-.
  43
  44 lemma cwhx_inv_lref (h) (G):
  45                     ∀L,i. ⦃G,L⦄ ⊢ ⬈[h] 𝐖𝐇⦃#i⦄ → ⊥.
  46 /2 width=7 by cwhx_inv_lref_aux/ qed-.
  47
  48 fact cwhx_inv_gref_aux (h) (G):
  49                        ∀Y,X. ⦃G,Y⦄ ⊢ ⬈[h] 𝐖𝐇⦃X⦄ →
  50                        ∀l. X = §l → ⊥.
  51 #h #G #Y #X * - X -Y
  52 [ #L #s #l #H destruct
  53 | #p #L #W #T #l #H destruct
  54 | #L #V #T #_ #l #H destruct
  55 ]
  56 qed-.
  57
  58 lemma cwhx_inv_gref (h) (G):
  59                     ∀L,l. ⦃G,L⦄ ⊢ ⬈[h] 𝐖𝐇⦃§l⦄ → ⊥.
  60 /2 width=7 by cwhx_inv_gref_aux/ qed-.
  61
  62 fact cwhx_inv_abbr_aux (h) (G):
  63                        ∀Y,X. ⦃G,Y⦄ ⊢ ⬈[h] 𝐖𝐇⦃X⦄ →
  64                        ∀V,T. X = +ⓓV.T → ⊥.
  65 #h #G #Y #X * - X -Y
  66 [ #L #s #X1 #X2 #H destruct
  67 | #p #L #W #T #X1 #X2 #H destruct
  68 | #L #V #T #_ #X1 #X2 #H destruct
  69 ]
  70 qed-.
  71
  72 lemma cwhx_inv_abbr (h) (G):
  73                     ∀Y,V,T. ⦃G,Y⦄ ⊢ ⬈[h] 𝐖𝐇⦃+ⓓV.T⦄ → ⊥.
  74 /2 width=8 by cwhx_inv_abbr_aux/ qed-.
  75
  76 fact cwhx_inv_ldef_aux (h) (G):
  77                        ∀Y,X. ⦃G,Y⦄ ⊢ ⬈[h] 𝐖𝐇⦃X⦄ →
  78                        ∀V,T. X = -ⓓV.T → ⦃G,Y.ⓓV⦄ ⊢ ⬈[h] 𝐖𝐇⦃T⦄.
  79 #h #G #Y #X * - X -Y
  80 [ #L #s #X1 #X2 #H destruct
  81 | #p #L #W #T #X1 #X2 #H destruct
  82 | #L #V #T #HT #X1 #X2 #H destruct //
  83 ]
  84 qed-.
  85
  86 lemma cwhx_inv_ldef (h) (G):
  87                     ∀Y,V,T. ⦃G,Y⦄ ⊢ ⬈[h] 𝐖𝐇⦃-ⓓV.T⦄ → ⦃G,Y.ⓓV⦄ ⊢ ⬈[h] 𝐖𝐇⦃T⦄.
  88 /2 width=3 by cwhx_inv_ldef_aux/ qed-.
  89
  90 fact cwhx_inv_appl_aux (h) (G):
  91                        ∀Y,X. ⦃G,Y⦄ ⊢ ⬈[h] 𝐖𝐇⦃X⦄ →
  92                        ∀V,T. X = ⓐV.T → ⊥.
  93 #h #G #Y #X * - X -Y
  94 [ #L #s #X1 #X2 #H destruct
  95 | #p #L #W #T #X1 #X2 #H destruct
  96 | #L #V #T #_ #X1 #X2 #H destruct
  97 ]
  98 qed-.
  99
 100 lemma cwhx_inv_appl (h) (G):
 101                     ∀Y,V,T. ⦃G,Y⦄ ⊢ ⬈[h] 𝐖𝐇⦃ⓐV.T⦄ → ⊥.
 102 /2 width=8 by cwhx_inv_appl_aux/ qed-.
 103
 104 fact cwhx_inv_cast_aux (h) (G):
 105                        ∀Y,X. ⦃G,Y⦄ ⊢ ⬈[h] 𝐖𝐇⦃X⦄ →
 106                        ∀U,T. X = ⓝU.T → ⊥.
 107 #h #G #Y #X * - X -Y
 108 [ #L #s #X1 #X2 #H destruct
 109 | #p #L #W #T #X1 #X2 #H destruct
 110 | #L #V #T #_ #X1 #X2 #H destruct
 111 ]
 112 qed-.
 113
 114 lemma cwhx_inv_cast (h) (G):
 115                     ∀Y,U,T. ⦃G,Y⦄ ⊢ ⬈[h] 𝐖𝐇⦃ⓝU.T⦄ → ⊥.
 116 /2 width=8 by cwhx_inv_cast_aux/ qed-.