reserve M for non empty set;
reserve V for ComplexNormSpace;
reserve f,f1,f2,f3 for PartFunc of M,V;
reserve z,z1,z2 for Complex;
reserve X,Y for set;

theorem Th35:
  f is total iff -f is total
proof
  thus f is total implies -f is total
  proof
    assume
A1: f is total;
    -f = (-1r)(#)f by Th23;
    hence thesis by A1,Th34;
  end;
  assume
A2: -f is total;
  -f = (-1r)(#)f by Th23;
  hence thesis by A2,Th34;
end;
