reserve r, s, t for Real;
reserve seq for Real_Sequence,
  X, Y for Subset of REAL;
reserve r3, r1, q3, p3 for Real;

theorem Th54:
  for X being Subset of REAL holds r in X iff 1/r in Inv X
proof
  let X be Subset of REAL;
  thus r in X implies 1/r in Inv X;
  assume 1/r in Inv X;
  then ex mr being Real st 1/r = 1/mr & mr in X;
  hence thesis by XCMPLX_1:59;
end;
