theorem Th32:
  for f being array of X st x in dom f & y in dom f
  holds Swap(f,x,y)/.y = f/.x
  proof
    let f be array of X;
    assume
A1: x in dom f & y in dom f;
    dom Swap(f,x,y) = dom f by FUNCT_7:99;
    hence Swap(f,x,y)/.y = Swap(f,x,y).y by A1,PARTFUN1:def 6
    .= f.x by A1,Th31 .= f/.x by A1,PARTFUN1:def 6;
  end;
