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 Th55:
  a>0 implies a #Q p / a #Q q = a #Q (p-q)
proof
  assume
A1: a>0;
  thus a #Q (p-q) = a #Q (p+-q) .= a #Q p * a #Q (-q) by A1,Th53
    .= a #Q p * (1/a #Q q) by A1,Th54
    .= a #Q p * 1 / a #Q q
    .= a #Q p / a #Q q;
end;
