This paper gives a mathematical approach to fault collapsing based on the stuck-at fault model for combinational circuits. The mathematical structure we work within is a Boolean ring of Boolean functions of several variables. The goal of fault collapsing for a given circuit is to reduce the number of stuck-at faults to be considered in test generation and fault diagnosis. For this purpose we need rules that let us eliminate faults from the considered fault set. In this paper some earlier known rules are proved in the new context, and several new rules are presented and proved. The most important of the new theorems deal with the relationship between stuck-at faults on a fanout stem and the branches. The concept of monotony of Boolean functions appears to be important in most of these new rules.