List-edge-colouring planar graphs with precoloured edges

Let $G$ be a simple planar graph of maximum degree $\mathrm{\Delta }$, let $t$ be a positive integer, and let $L$ be an edge list assignment on $G$ with $|L(e)| \geq \Delta+t$forall$e \in E(G)$\mathrm{.}Weprovethatif$H$isasubgraphof$G$thathasbeen$L$-edge-coloured, then the edge-precolouring can be extended to an $L$-edge-colouring of $G$, provided that $H$ has maximum degree $d\le t$ and either $d\le t-4$ or $\mathrm{\Delta }$ is large enough ($\mathrm{\Delta }\ge 16+d$ suffices). If $d>t$, there are examples for any choice of $\mathrm{\Delta }$ where the extension is impossible.