reserve n,n1,n2,m for Nat,
  r,r1,r2,p,g1,g2,g for Real,
  seq,seq9,seq1 for Real_Sequence,
  y for set;

theorem Th2:
  g<>0 & r<>0 implies |.g"-r".|=|.g-r.|/(|.g.|*|.r.|)
proof
  assume that
A1: g<>0 and
A2: r<>0;
  thus |.g"-r".|=|.1/g-r".| by XCMPLX_1:215
    .=|.1/g-1/r.| by XCMPLX_1:215
    .=|.(1*r-1*g)/(g*r).| by A1,A2,XCMPLX_1:130
    .=|.r-g.|/|.g*r.| by COMPLEX1:67
    .=|.-(g-r).|/(|.g.|*|.r.|) by COMPLEX1:65
    .=|.g-r.|/(|.g.|*|.r.|) by COMPLEX1:52;
end;
