There is no loss of generality in assuming that......
This involves no loss of generality.
Without loss of generality we can assume that......
[In many cases, the phrase ”without loss of generality” can be omitted: write simply: We can clearly assume that...... Do not use the abbreviation “w.l.o.g.'']
Without losing any generality, we could have restricted our definition of integration to integrals over all of X. [Not: “Without loosing'']
It simplifies the argument, and causes no loss of generality, to assume......
A completely different method was used to establish Theorem 2 in full generality.
Rather than discuss this in full generality, let us look at a particular situation of this kind.
A number of authors have considered, in varying degrees of generality, the problem of determining......
It seems preferable, for clarity's sake, not to present the construction at the outset in the greatest generality possible.
It seems that the relations between these concepts emerge most clearly when the setting is quite abstract, and this (rather than a desire for mere generality) motivates our approach to the subject.