let X, Y be set ; :: thesis: for C being non empty set
for V being RealNormSpace
for f1, f2 being PartFunc of C,the carrier of V st f1 is_bounded_on X & f2 | Y is V8() holds
f1 + f2 is_bounded_on X /\ Y
let C be non empty set ; :: thesis: for V being RealNormSpace
for f1, f2 being PartFunc of C,the carrier of V st f1 is_bounded_on X & f2 | Y is V8() holds
f1 + f2 is_bounded_on X /\ Y
let V be RealNormSpace; :: thesis: for f1, f2 being PartFunc of C,the carrier of V st f1 is_bounded_on X & f2 | Y is V8() holds
f1 + f2 is_bounded_on X /\ Y
let f1, f2 be PartFunc of C,the carrier of V; :: thesis: ( f1 is_bounded_on X & f2 | Y is V8() implies f1 + f2 is_bounded_on X /\ Y )
assume A1: ( f1 is_bounded_on X & f2 | Y is V8() ) ; :: thesis: f1 + f2 is_bounded_on X /\ Y
then f2 is_bounded_on Y by Th61;
hence f1 + f2 is_bounded_on X /\ Y by A1, Th53; :: thesis: verum