English
If φ is monotone on t, ψ is a right inverse of φ on s, and ψ maps s into t, then ψ is monotone on s (in the Function sense).
Русский
Если φ монотонна на t, ψ является правым обратным к φ на s, и ψ отображает s в t, то ψ монотонна на s (в терминах функции).
LaTeX
$$$\operatorname{MonotoneOn}(\varphi,t) \to \operatorname{RightInvOn}(\psi,\varphi,s) \to \operatorname{MapsTo}(\psi,s,t) \Rightarrow \operatorname{MonotoneOn}(\psi,s)$$$
Lean4
/-- `Set.mulAntidiagonal s t a` is the set of all pairs of an element in `s` and an element in `t`
that multiply to `a`. -/
@[to_additive /-- `Set.addAntidiagonal s t a` is the set of all pairs of an element in `s` and an
element in `t` that add to `a`. -/
]
def mulAntidiagonal (s t : Set α) (a : α) : Set (α × α) :=
{x | x.1 ∈ s ∧ x.2 ∈ t ∧ x.1 * x.2 = a}
