reserve a,b,r for Real;
reserve A,B for non empty set;
reserve f,g,h for Element of PFuncs(A,REAL);

theorem Th17:
  (multrealpfunc A).(1,f) = f
proof
  reconsider g = (multrealpfunc A).(jj,f) as Element of PFuncs(A,REAL);
A1: now
    let x be Element of A;
    assume x in dom f;
    hence g.x = 1*(f.x) by Th9
      .= f.x;
  end;
  dom g=dom f by Th9;
  hence thesis by A1,PARTFUN1:5;
end;
