This is not a duplicate of Why are there two articles in front of a noun?, because this time both articles are not pronouns, but real articles.
Nachdem die Schutzleute eine Weile überlegt hatten, gingen sie runter und holten eine Leiter, die sie an dem einen Hausgiebel aufstellte (…) und unter Geschrei und Gelächter lief sie (Pippi) den Dachfirst entlang zum anderen Giebel hin. source
A German friend of mine said that, yes, they are really articles, and the second one only shows that that Giebel (facade) is only one. But later in the text, another one appears, so that explanation doesn’t work. (The friend is a programmer, not a linguist.)
Why are there two articles?
Why are they in different cases?
If the construction is correct, what is the rule, how should those be constructed and when should we use them?
A reference to some grammar source would be highly appreciated.
Maybe, it is some intentional rule breaking for to express an emotion?
Or, maybe it is a part of the modern language (the source is the year 2004) not fitting to classical rules? For example, in Czech it easily could happen.