reserve i,j,k,n,n1,n2,m for Nat;
reserve a,r,x,y for Real;
reserve A for non empty closed_interval Subset of REAL;
reserve C for non empty set;
reserve X for set;

theorem Th13:
  for f being Function of C,REAL holds max+(f) is total & max-(f)
  is total
proof
  let f be Function of C,REAL;
A1: dom f = C by FUNCT_2:def 1;
  then
A2: dom max-(f) = C by RFUNCT_3:def 11;
  dom max+(f) = C by A1,RFUNCT_3:def 10;
  hence thesis by A2,PARTFUN1:def 2;
end;
