reserve a,a1,a2,b,c,d for Ordinal,
  n,m,k for Nat,
  x,y,z,t,X,Y,Z for set;
reserve f,g for Function;
reserve A,B,C for array;

theorem Th33:
 for x,y,z being object holds
  z <> x & z <> y implies Swap(f,x,y).z = f.z
  proof let x,y,z be object;
assume
A1: z <> x & z <> y;
    per cases;
    suppose
      x in dom f & y in dom f; then
      Swap(f,x,y) = f+*(x,f.y)+*(y,f.x) by FUNCT_7:def 12;
      hence Swap(f,x,y).z = (f+*(x,f.y)).z by A1,FUNCT_7:32
      .= f.z by A1,FUNCT_7:32;
    end;
    suppose
      not (x in dom f & y in dom f);
      hence Swap(f,x,y).z = f.z by FUNCT_7:def 12;
    end;
  end;
