let F be Function of T,R^1; :: thesis: ( F = f + g implies F is continuous )
assume A1: F = f + g ; :: thesis: F is continuous
consider h being Function of T,R^1 such that
A2: for p being Point of T
for r1, r2 being Real st f . p = r1 & g . p = r2 holds
h . p = r1 + r2 and
A3: h is continuous by JGRAPH_2:19;
F = h

proof

let x be Point of T; :: according to FUNCT_2:def 8 :: thesis: F . x = h . x
thus F . x = (f . x) + (g . x) by A1, VALUED_1:1
.= h . x by A2 ; :: thesis: verum

end;

hence F is continuous by A3; :: thesis: verum