reserve D for non empty set,
  f for FinSequence of D,
  p, p1, p2, p3, q for Element of D,
  i, j, k, l, n for Nat;

theorem Th33:
  i <> k & j <> k & 1 <= i & i <= len f & 1 <= j & j <= len f
  implies Swap(Replace(f, k, p), i, j) = Replace(Swap(f, i, j), k, p)
proof
  assume that
A1: i <> k and
A2: j <> k and
A3: 1 <= i and
A4: i <= len f and
A5: 1 <= j and
A6: j <= len f;
  i <= len Replace(f, k, p) & j <= len Replace(f, k, p) by A4,A6,FUNCT_7:97;
  hence Swap(Replace(f, k, p), i, j) = Replace(Replace(Replace(f, k, p), i,
  Replace(f, k, p)/.j), j, Replace(f, k, p)/.i) by A3,A5,Def2
    .= Replace(Replace( Replace(f, k, p), i, f/.j), j, Replace(f, k, p)/.i)
  by A2,A5,A6,Th10
    .= Replace(Replace(Replace(f, k, p), i, f/.j), j, f/.i) by A1,A3,A4,Th10
    .= Replace(Replace(Replace(f, i, f/.j), k, p), j, f/.i) by A1,FUNCT_7:33
    .= Replace(Replace(Replace(f, i, f/.j), j, f/.i), k, p) by A2,FUNCT_7:33
    .= Replace(Swap(f, i, j), k, p) by A3,A4,A5,A6,Def2;
end;
