reserve a,x,y for object, A,B for set,
  l,m,n for Nat;
reserve X,Y for set, x for object,
  p,q for Function-yielding FinSequence,
  f,g,h for Function;
reserve m,n,k for Nat, R for Relation;
reserve i,j for Nat;
reserve F for Function,
  e,x,y,z for object;

theorem Th98:
 for x,y being object holds dom Swap(F,x,y) = dom F
proof let x,y be object;
  per cases;
  suppose
    x in dom F & y in dom F;
    hence dom Swap(F,x,y) = dom(F+*(x,F.y)+*(y,F.x)) by Def11
      .= dom(F+*(x,F.y)) by Th29
      .= dom F by Th29;
  end;
  suppose
    not(x in dom F & y in dom F);
    hence thesis by Def11;
  end;
end;
