matita/matita/contribs/lambdadelta/basic_2/substitution/llor.ma

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  14
  15 include "basic_2/notation/relations/lazyor_4.ma".
  16 include "basic_2/substitution/frees.ma".
  17
  18 (* POINTWISE UNION FOR LOCAL ENVIRONMENTS ***********************************)
  19
  20 definition llor: relation4 term lenv lenv lenv ≝ λT,L2,L1,L.
  21                  ∧∧ |L1| ≤ |L2| & |L1| = |L|
  22                   & (∀I1,I2,I,K1,K2,K,V1,V2,V,i.
  23                        ⇩[i] L1 ≡ K1.ⓑ{I1}V1 → ⇩[i] L2 ≡ K2.ⓑ{I2}V2 → ⇩[i] L ≡ K.ⓑ{I}V →
  24                        (∧∧ (L1 ⊢ i ϵ 𝐅*[yinj 0]⦃T⦄ → ⊥) & I1 = I & V1 = V) ∨
  25                        (∧∧ L1 ⊢ i ϵ 𝐅*[yinj 0]⦃T⦄  & I1 = I & V2 = V)
  26                     ).
  27
  28 interpretation
  29    "lazy union (local environment)"
  30    'LazyOr L1 T L2 L = (llor T L2 L1 L).
  31
  32 (* Basic properties *********************************************************)
  33
  34 lemma llor_atom: ∀T,L2. ⋆ ⩖[T] L2 ≡ ⋆.
  35 #T #L2 @and3_intro //
  36 #I1 #I2 #I #K1 #K2 #K #V1 #V2 #V #i #HLK1
  37 elim (ldrop_inv_atom1 … HLK1) -HLK1 #H destruct
  38 qed.