  When a proposition has no proof in an inference system, it is sometimes
useful to build a counter-proof explaining, step by step, the reason of this
non-provability. In general, this counter-proof is a (possibly) infinite
co-inductive proof in a different inference system. In this paper, we show
that, for some decidable inference systems, this (possibly) infinite proof has
a representation as a finite proof in yet another system, equivalent to the
previous one.
