\begin{definition}[Definition:Extremal Embedding in Field of Functional]
Let $J$ be a functional such that:
:$\ds J \sqbrk {\mathbf y} = \int_a^b \map F {x, \mathbf y, \mathbf y'} \rd x$
Let $\gamma$ be an extremal of $J$.
{{explain|Extremum or extremal?}}
Let $R$ be a simply connected open region which contains $\gamma$ as a subset.
{{explain|GF puts "open" in brackets; does it matter?}}
Let a field of functional $J$ be defined at every point of $R$.
Let one of the trajectories of the field be $\gamma$.
Then $\gamma$ can be '''embedded''' in a field of functional $J$.
{{explain|If $\gamma$ "can be" embedded, is it correct to say that $\gamma$ "is" embedded? If not, then is it more grammatically accurate to define $\gamma$ as being "embeddable"? Otherwise it looks as though "can be" introduces a statement that needs to be proven.}}
\end{definition}