
theorem Th5:
for X be set, f be PartFunc of X,REAL st f is nonpositive holds
  -f is nonnegative
proof
    let X be set, f be PartFunc of X,REAL;
    assume A1: f is nonpositive;

    now let x be object;
     assume x in dom(-f); then
     f.x <= 0 by A1,MESFUNC6:53; then
     -(f.x) >= 0;
     hence 0 <= (-f).x by VALUED_1:8;
    end;
    hence -f is nonnegative by MESFUNC6:52;
end;
