The objective of the paper is to make rigorous a development that was presented in a previous article. In particular we want to justify the steps of that development that led to negation of Special Relativity Theory. In that article, a simple medium with loss (medium (I), to which is attached a frame K) was considered interfaced by a perfect electric conductor filling a half space (medium (II), to which is attached a frame K') that is in uniform rectilinear motion with respect to medium (I). It is noted that the result obtained by taking the difference of dispersion relations for incident and reflected waves is actually a simultaneous solution of the two dispersion relations for frequency omega' and wave number k(1)'. It is indicated that because of the loss in the medium, the solution set (omega', k(1)') is non-zero and a relation exists to falsify the Special Relativity Theory. When the loss is nullified, the only simultaneous solution of the two dispersion relations becomes the trivial solution omega' = k(1)' = 0 and no relation exists to negate the Special Relativity Theory. The relation used to argue against the Special Relativity Theory involves frequency omega' measured from K', v the speed of K' with respect to K, speed of light in vacuum c and the constitutive parameters of medium (I); epsilon(1), mu(1), sigma(1). It is thus shown that c depends on frequency and by rewriting the said relation employing an expression for omega' in terms of v, c and the incident wave parameters, it is shown at c depends on v too. Alternatively the solution for k(1)' is used in a similar manner and it is demonstrated that this expression can also be used to falsify the Special Relativity Theory.