let X, Y be set ; :: thesis: for C being non empty set
for f1, f2 being PartFunc of C,COMPLEX st f1 | X is bounded & f2 | Y is constant holds
(f1 + f2) | (X /\ Y) is bounded
let C be non empty set ; :: thesis: for f1, f2 being PartFunc of C,COMPLEX st f1 | X is bounded & f2 | Y is constant holds
(f1 + f2) | (X /\ Y) is bounded
let f1, f2 be PartFunc of C,COMPLEX; :: thesis: ( f1 | X is bounded & f2 | Y is constant implies (f1 + f2) | (X /\ Y) is bounded )
assume that
A1: f1 | X is bounded and
A2: f2 | Y is constant ; :: thesis: (f1 + f2) | (X /\ Y) is bounded
f2 | Y is bounded by A2, Th80;
hence (f1 + f2) | (X /\ Y) is bounded by A1, Th74; :: thesis: verum