reserve x for set;
reserve a, b, c for Real;
reserve m, n, m1, m2 for Nat;
reserve k, l for Integer;
reserve p, q for Rational;
reserve s1, s2 for Real_Sequence;

theorem Th1:
  s1 is convergent & (for n holds s1.n>=a) implies lim s1 >= a
proof
  assume that
A1: s1 is convergent and
A2: for n holds s1.n>=a;
  set s = seq_const a;
A3: now
    let n;
    s1.n >= a by A2;
    hence s1.n >= s.n by SEQ_1:57;
  end;
  lim s = s.0 by SEQ_4:26
    .= a by SEQ_1:57;
  hence thesis by A1,A3,SEQ_2:18;
end;
