English
The equality dlookup on kunion equals some value b is equivalent to either dlookup on the first list equals some b or (a not in the first keys and dlookup on the second list equals some b).
Русский
Равенство dlookup на kunion равно (некоторому) b эквивалентно либо dlookup на первой лисtе равно some b, либо (a не в keys первой ленты и dlookup на второй ленте равно some b).
LaTeX
$$$ dlookup\\ a\\ (kunion\\ l_1\\ l_2) = \\text{some } b \\iff dlookup\\ a\\ l_1 = \\text{some } b \\lor (a \\notin l_1.\\keys \\land dlookup\\ a\\ l_2 = \\text{some } b) $$$
Lean4
@[simp]
theorem dlookup_kunion_eq_some {a} {b : β a} {l₁ l₂ : List (Sigma β)} :
dlookup a (kunion l₁ l₂) = some b ↔ dlookup a l₁ = some b ∨ a ∉ l₁.keys ∧ dlookup a l₂ = some b :=
mem_dlookup_kunion
