
theorem Th9:
  for I being 2-element set, f being ManySortedSet of I
  for i,j being Element of I st i <> j holds f = (i,j) --> (f.i,f.j)
proof
  let I be 2-element set, f be ManySortedSet of I;
  let i,j be Element of I;
  assume A1: i <> j;
  dom f = I by PARTFUN1:def 2
    .= {i,j} by A1, Th8;
  hence thesis by FUNCT_4:66;
end;
