4.8.1 Premise for Dividing into Cases
We have some warnings for you here. This case is used as a premise when dividing a formula x=1 or x=2 or not (x=1 & x=2) ---(1) into cases. It means that this division of cases covers all cases. When dividing into cases in this way, we have to state that we are stating this about all cases.
In addition, like the upper example, when formation of formula (1) is clear, "by" behind "now per cases" is unnecessary.