English
Let p and q be subsets. The degree of their disjoint union equals the sum of their degrees: the degree of p ⊕' q is the sum of the degrees of p and q.
Русский
Пусть p и q — множества. Степень их дизъюнктивного объединения равна сумме степеней p и q: степень p ⊕' q равна степени p плюс степень q.
LaTeX
$$$$ \\operatorname{of}(p \\oplus' q) = \\operatorname{of}(p) + \\operatorname{of}(q). $$$$
Lean4
@[simp]
theorem add_of (p : Set α) (q : Set β) : of (p ⊕' q) = of p + of q :=
of_eq_of.mpr
⟨disjoin_manyOneReducible (manyOneReducible_toNat.trans OneOneReducible.disjoin_left.to_many_one)
(manyOneReducible_toNat.trans OneOneReducible.disjoin_right.to_many_one),
disjoin_manyOneReducible (toNat_manyOneReducible.trans OneOneReducible.disjoin_left.to_many_one)
(toNat_manyOneReducible.trans OneOneReducible.disjoin_right.to_many_one)⟩
