theorem
  seq is constant iff for n,m holds seq.n = seq.m
proof
  thus seq is constant implies for n,m holds seq.n = seq.m by VALUED_0:23;
  assume that
A1: for n,m holds seq.n = seq.m and
A2: seq is non constant;
  now
    let n be Nat;
    consider n1 be Nat such that
A3: seq.n1 <> seq.n by A2,VALUED_0:def 18;
    thus contradiction by A1,A3;
  end;
  hence thesis;
end;
