(* POINTWISE UNION FOR LOCAL ENVIRONMENTS ***********************************)
definition llor: ynat → relation4 term lenv lenv lenv ≝ λd,T,L2,L1,L.
(* POINTWISE UNION FOR LOCAL ENVIRONMENTS ***********************************)
definition llor: ynat → relation4 term lenv lenv lenv ≝ λd,T,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) |
& (∀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) |
(* Basic properties *********************************************************)
(* Note: this can be proved by llor_skip *)
(* Basic properties *********************************************************)
(* Note: this can be proved by llor_skip *)
-lemma llor_atom: ∀L2,T,d. ⋆ ⩖[T, d] L2 ≡ ⋆.
-#L2 #T #d @and3_intro //
+lemma llor_atom: ∀T,d. ⋆ ⩖[T, d] ⋆ ≡ ⋆.
+#T #d @and3_intro //