theorem
  seq1 is constant & seq2 is constant & seq = seq1 + seq2 implies
  seq is constant
proof
  assume that
A1: seq1 is constant and
A2: seq2 is constant and
A3: seq = seq1 + seq2;
  consider x such that
A4: for n being Nat holds seq1.n = x by A1;
  consider y such that
A5: for n being Nat holds seq2.n = y by A2;
  take z = x + y;
  let n be Nat;
  thus seq.n = seq1.n + seq2.n by A3,NORMSP_1:def 2
    .= x + seq2.n by A4
    .= z by A5;
end;
