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 Th30:
  for f being array of X st x in dom f & y in dom f
  holds Swap(f,x,y)/.x = f/.y
  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)/.x = Swap(f,x,y).x by A1,PARTFUN1:def 6
    .= f.y by A1,Th29 .= f/.y by A1,PARTFUN1:def 6;
  end;
