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 Th77:
  a > 0 implies a #R (b-c) = a #R b / a #R c
proof
  assume
A1: a > 0;
  thus a #R (b-c) = a #R (b + -c) .= a #R b * a #R (-c) by A1,Th75
    .= a #R b * (1 / a #R c) by A1,Th76
    .= a #R b * (1 * (a #R c)")
    .= a #R b / a #R c;
end;
