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
  a > 1 & b < 0 implies a #R b < 1
proof
  assume that
A1: a>1 and
A2: b<0;
  -b>0 by A2;
  then a #R (-b) > 1 by A1,Th86;
  then 1 / a #R b > 1 by A1,Th76;
  then 1 / (1 / a #R b) < 1 by XREAL_1:212;
  hence thesis;
end;
