The most commonly used expressions:
Without loss of generality
WOLOG / WLOG / w.l.o.g
Without any loss of generality
With no loss of generality
There is no loss of generality in that/our assumption.
Besides:
This assumption does not diminish the generality.
This assumption does not limit the genetality.
This assumption does not compromise the generality.
This assumption does not restrict the generality.
This assumption does not curcumscribe the generality.
This assumption does not result in loss of generality. (or any loss of generality)
This assumption does not lead to loss of generality.
This assumption does not cause loss of generality.
This assumption does not entail loss of generality.
This assumption does not affect the generality.
This assumption does not involve any loss of generality.
This assumption does not lose the generality.
This assumption does not influence the generality.