matita/matita/contribs/lambda_delta/Basic_2/substitution/gdrop.ma

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  14
  15 include "Basic_2/substitution/ldrop.ma".
  16
  17 (* GLOBAL ENVIRONMENT SLICING ***********************************************)
  18
  19 inductive gdrop (e:nat) (G1:lenv) : predicate lenv ≝
  20 | gdrop_lt: ∀G2. e < |G1| → ⇓[0, |G1| - (e + 1)] G1 ≡ G2 → gdrop e G1 G2
  21 | gdrop_ge: |G1| ≤ e → gdrop e G1 (⋆)
  22 .
  23
  24 interpretation "global slicing" 'RGDrop e G1 G2 = (gdrop e G1 G2).
  25
  26 (* basic inversion lemmas ***************************************************)
  27 (*
  28 fact gdrop_inv_atom2_aux: ∀G1,G2,e. ⇓[e] G1 ≡ G2 → G2 = ⋆ → |G1| ≤ e.
  29 #G1 #G2 #e * -G2 //
  30 #G2 #He #HG12 #H destruct
  31 lapply (ldrop_fwd_O1_length … HG12) -HG12
  32 >minus_le_minus_minus_comm // -He >le_plus_minus_comm // <minus_n_n
  33 >(commutative_plus e) normalize #H destruct
  34 qed.
  35
  36 lemma gdrop_inv_atom2: ∀G1,e. ⇓[e] G1 ≡ ⋆ → |G1| ≤ e.
  37 /2 width=3/ qed-.
  38
  39 lemma gdrop_inv_ge: ∀G1,G2,e. ⇓[e] G1 ≡ G2 → |G1| ≤ e → G2 = ⋆.
  40 #G1 #G2 #e * // #G2 #H1 #_ #H2
  41 lapply (lt_to_le_to_lt … H1 H2) -H1 -H2 #He
  42 elim (lt_refl_false … He)
  43 qed-.
  44 *)