reserve A for non empty closed_interval Subset of REAL;

theorem
for c being Real, f,g be Function of REAL,REAL st
f | A is bounded & g | A is bounded
holds
( (f|].-infty,c.]) +* (g|[.c,+infty.[) ) | A is bounded
proof
 let c be Real, f,g be Function of REAL,REAL;
 assume f | A is bounded & g | A is bounded; then
 ( (f|].-infty,c.[) +* (g|[.c,+infty.[) ) | A is bounded by Th18X;
 hence thesis by Th18E;
end;
