  Formal proof checkers such as Coq are capable of validating proofs of
correction of algorithms for finite field arithmetics but they require
extensive training from potential users. The delayed solution of a triangular
system over a finite field mixes operations on integers and operations on
floating point numbers. We focus in this report on verifying proof obligations
that state that no round off error occurred on any of the floating point
operations. We use a tool named Gappa that can be learned in a matter of
minutes to generate proofs related to floating point arithmetic and hide
technicalities of formal proof checkers. We found that three facilities are
missing from existing tools. The first one is the ability to use in Gappa new
lemmas that cannot be easily expressed as rewriting rules. We coined the second
one ``variable interchange'' as it would be required to validate loop
interchanges. The third facility handles massive loop unrolling and argument
instantiation by generating traces of execution for a large number of cases. We
hope that these facilities may sometime in the future be integrated into
mainstream code validation.
