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15 include "basic_2/notation/relations/lazyor_4.ma".
16 include "basic_2/multiple/frees.ma".
18 (* POINTWISE UNION FOR LOCAL ENVIRONMENTS ***********************************)
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)
29 "lazy union (local environment)"
30 'LazyOr L1 T L2 L = (llor T L2 L1 L).
32 (* Basic properties *********************************************************)
34 lemma llor_atom: ∀T,L2. ⋆ ⩖[T] L2 ≡ ⋆.
36 #I1 #I2 #I #K1 #K2 #K #V1 #V2 #V #i #HLK1
37 elim (ldrop_inv_atom1 … HLK1) -HLK1 #H destruct