reserve n,m for Nat,
  r,r1,r2,s,t for Real,
  x,y for set;

theorem
  for F be PartFunc of REAL,REAL, X be set st F is_convex_on X holds
  max+ F is_convex_on X
proof
  let F be PartFunc of REAL,REAL, X be set;
  assume F is_convex_on X;
  then max+(F - 0) is_convex_on X by Th59;
  hence thesis by Th48;
end;
