multline inside an item

The amsmath alignment environments are only for display math. But mathtools augments the available environments:

\documentclass[a4paper]{article}
\usepackage{mathtools,enumerate,amssymb}
\begin{document}

\begin{enumerate}[i.]
    \item $\mathit{checkorder}( (\lambda,\lambda,\lambda) ) \triangleq \mathit{true}$
    \item $\begin{multlined}[t]
     \mathit{checkorder}( (a,(u,U_1,U_2),(v,V_1,V_2)) ) \triangleq \\
     (u = \lambda \vee u \leq_A a) \wedge
     (v = \lambda \vee a \leq_A v) \wedge {} \\
     \mathit{checkorder}(U_1) \wedge \mathit{checkorder}(U_2) \wedge
     \mathit{checkorder}(V_1) \wedge checkorder(V_2)
     \end{multlined}$
    \item $\mathit{checkorder}(T) \triangleq \mathit{false}$ negli altri casi
\end{enumerate}
\end{document}

Notice a couple of refinements: long function names should be inside \mathit, to get a better looking font in this case; the \wedge before \\ should be followed by {} to get correct spacing.

Never use $$ in LaTeX.

I had a similar issue with \multline environment. So I came up with a forced solution. Here is what I did:

\item \abovedisplayskip-15pt 
      \belowdisplayskip\abovedisplayskip
      \begin{setlength}{\multlinegap}{0pt}
         \begin{multline*}
           2(x^2y-2xy^3+6xy)-3(-5xy+3x^2y\\-7xy^3)
            +5(xy^3-xy+x^2y)
      \end{multline*}
      \end{setlength}

Of course, egreg's solution is by far the best and mine is was just out of desperation in finding an immediate solutions. I know that my code above is not the best but hey it solved my problem. I have decided to implement egreg's answer into my code as it seems to better and more concise.