(* POINTWISE UNION FOR LOCAL ENVIRONMENTS ***********************************)
definition llor: ynat → relation4 term lenv lenv lenv ≝ λd,T,L2,L1,L.
- ∧∧ |L1| ≤ |L2| & |L1| = |L|
+ ∧∧ |L1| = |L2| & |L1| = |L|
& (∀I1,I2,I,K1,K2,K,V1,V2,V,i.
⇩[i] L1 ≡ K1.ⓑ{I1}V1 → ⇩[i] L2 ≡ K2.ⓑ{I2}V2 → ⇩[i] L ≡ K.ⓑ{I}V → ∨∨
(∧∧ yinj i < d & I1 = I & V1 = V) |
(∧∧ (L1 ⊢ i ϵ 𝐅*[d]⦃T⦄ → ⊥) & I1 = I & V1 = V) |
- (∧∧ d ≤ yinj i & L1 ⊢ i ϵ 𝐅*[d]⦃T⦄ & I1 = I & V2 = V)
+ (∧∧ d ≤ yinj i & L1 ⊢ i ϵ 𝐅*[d]⦃T⦄ & I2 = I & V2 = V)
).
interpretation
(* Basic properties *********************************************************)
-lemma llor_atom: ∀L2,T,d. ⋆ ⩖[T, d] L2 ≡ ⋆.
-#L2 #T #d @and3_intro //
+(* Note: this can be proved by llor_skip *)
+lemma llor_atom: ∀T,d. ⋆ ⩖[T, d] ⋆ ≡ ⋆.
+#T #d @and3_intro //
#I1 #I2 #I #K1 #K2 #K #V1 #V2 #V #i #HLK1
-elim (ldrop_inv_atom1 … HLK1) -HLK1 #H destruct
+elim (drop_inv_atom1 … HLK1) -HLK1 #H destruct
qed.