reserve X for non empty UNITSTR;
reserve a, b for Real;
reserve x, y for Point of X;
reserve X for RealUnitarySpace;
reserve x, y, z, u, v for Point of X;
reserve seq, seq1, seq2, seq3 for sequence of X;
reserve  n for Nat;

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