The file Euclidean.m already contains a definition for dE. When you try to define dE[t_]:=de, that dE gets evaluated and so your definition is actually trying to create a downvalue for that entire piecewise expression. But Piecewise is protected, so redefining it isn't allowed.
You can plot the piecewise function directly:
Plot[dE, {t, 0, 2}]
If you really want a new function, you could do something like this:
newDE = dE /. t -> # &
but I don't really recommend that.
