reserve x for object, X,Y for set;
reserve C for non empty set;
reserve c for Element of C;
reserve f,f1,f2,f3,g,g1 for complex-valued Function;
reserve r,p for Complex;

theorem Th26:
  f^^ = f|(dom (f^))
proof
A1: dom (f^^) = dom (f|(dom (f^))) by Th6;
  now
    let c be object;
    assume
A2: c in dom (f^^);
    then c in dom f /\ dom (f^) by A1,RELAT_1:61;
    then
A3: c in dom (f^) by XBOOLE_0:def 4;
    thus (f^^).c = ((f^).c)" by A2,Def2
      .= ((f.c)")" by A3,Def2
      .= (f|(dom (f^))).c by A1,A2,FUNCT_1:47;
  end;
  hence thesis by A1,FUNCT_1:2;
end;
