theorem
  seq1 is constant implies a * seq1 is constant
proof
  assume
A1: seq1 is constant;
    set seq = a * seq1;
  consider x such that
A2: for n being Nat holds seq1.n = x by A1;
  take z = a * x;
  let n be Nat;
  thus seq.n = a * seq1.n by NORMSP_1:def 5
    .= z by A2;
end;
