matita/matita/contribs/lambdadelta/basic_2A/multiple/llor.ma

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  14
  15 include "ground_2/xoa/and_4.ma".
  16 include "basic_2A/notation/relations/lazyor_5.ma".
  17 include "basic_2A/multiple/frees.ma".
  18
  19 (* POINTWISE UNION FOR LOCAL ENVIRONMENTS ***********************************)
  20
  21 definition llor: ynat → relation4 term lenv lenv lenv ≝ λl,T,L2,L1,L.
  22                  ∧∧ |L1| = |L2| & |L1| = |L|
  23                   & (∀I1,I2,I,K1,K2,K,V1,V2,V,i.
  24                        ⬇[i] L1 ≡ K1.ⓑ{I1}V1 → ⬇[i] L2 ≡ K2.ⓑ{I2}V2 → ⬇[i] L ≡ K.ⓑ{I}V → ∨∨
  25                        (∧∧ yinj i < l & I1 = I & V1 = V) |
  26                        (∧∧ (L1 ⊢ i ϵ 𝐅*[l]⦃T⦄ → ⊥) & I1 = I & V1 = V) |
  27                        (∧∧ l ≤ yinj i & L1 ⊢ i ϵ 𝐅*[l]⦃T⦄ & I2 = I & V2 = V)
  28                     ).
  29
  30 interpretation
  31    "lazy union (local environment)"
  32    'LazyOr L1 T l L2 L = (llor l T L2 L1 L).
  33
  34 (* Basic properties *********************************************************)
  35
  36 (* Note: this can be proved by llor_skip *)
  37 lemma llor_atom: ∀T,l. ⋆ ⋓[T, l] ⋆ ≡ ⋆.
  38 #T #l @and3_intro //
  39 #I1 #I2 #I #K1 #K2 #K #V1 #V2 #V #i #HLK1
  40 elim (drop_inv_atom1 … HLK1) -HLK1 #H destruct
  41 qed.