  It is shown how dual space diagrammatic representation of momentum integrals
corresponding to triangle ladder diagrams with an arbitrary number of rungs can
be transformed to half-diamonds. In paper arXiv:0803.3420 [hep-th] the
half-diamonds were related by conformal integral substitution to the diamonds
which represent the dual space image of four-point ladder integrals in the
four-dimensional momentum space. Acting in the way described in the present
paper we do not need to use the known result for diamond (four-point) diagrams
as an external input in deriving relations of arXiv:0803.3420 [hep-th],
however, that result for the diamond diagram arises in the present proof as an
intermediate consequence in a step-by-step diagrammatic transformation from the
triangle ladder diagram to the half-diamond diagrams.
