let F be Function of T,R^1; :: thesis: ( F = f + r implies F is continuous )
assume A1: F = f + r ; :: thesis: F is continuous
consider g being Function of T,R^1 such that
A2: for p being Point of T
for s being Real st f . p = s holds
g . p = s + r and
A3: g is continuous by JGRAPH_2:24;
F = g
proof
let x be Point of T; :: according to FUNCT_2:def 8 :: thesis: F . x = g . x
thus F . x = (f . x) + r by A1, VALUED_1:2
.= g . x by A2 ; :: thesis: verum
end;
hence F is continuous by A3; :: thesis: verum