reserve a,b,c,d for Real;
reserve r,s for Real;

theorem
  for a,b st b <> 0 ex c st a = b/c
proof
  let a,b;
  assume
A1: b <> 0;
  then consider c being Complex such that
A2: a = b/c by XCMPLX_1:232;
  per cases;
  suppose c = 0;
    hence thesis by A2;
  end;
  suppose c <> 0;
    then c = b/a by A1,A2,XCMPLX_1:54;
    then reconsider c as Real;
    take c;
    thus thesis by A2;
  end;
end;
