The rainbow version of Rosa's graceful tree conjecture

For $X\subseteq\mathbb{N}$, let $K_X$ be the complete graph on vertex set $X$ in which each edge $ij$ has colour $|i-j|$. Write $[n]=\{1,\ldots,n\}$. A copy of a tree in this edge-coloured graph is rainbow if all its edges receive distinct colours. Rainbow version of Rosa's graceful tree conjecture. $K_{[n]}$ contains a rainbow copy of every $n$-vertex tree $T$. This is equivalent to the graceful tree conjecture: an injective map from the vertices of $T$ into $[n]$ gives an embedding in $K_{[n]}$, and the embedding is rainbow exactly when the map is a graceful labelling. Thus the statement is a reformulation rather than a separate conjecture.