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
  1 < i & i <= len f implies Swap(f, 1, i) = <*f/.i*>^((f/^1)|(i-'2))^<*
  f/.1*>^(f/^i)
proof
  assume 1 < i & i <= len f; then
  Swap(f,1,i) = (f|(1-'1))^<*f/.i*>^(f/^1)|(i-'1-'1)^<*f/.1*>^(f/^i) by Th27
    .= (f|0)^<*f/.i*>^(f/^1)|(i-'1-'1)^<*f/.1*>^(f/^i) by XREAL_1:232
    .= <*f/.i*>^(f/^1)|(i-'1-'1)^<*f/.1*>^(f/^i) by FINSEQ_1:34;
  hence thesis by NAT_D:45;
end;
