theorem Th216:
  a <> 0 & a///A c= a///B implies A c= B
proof
  assume that
A1: a <> 0 and
A2: a///A c= a///B;
  let z;
  assume z in A;
  then a/z in a///A by Th213;
  then consider c such that
A3: a/z = a/c and
A4: c in B by A2,Th215;
  z" = c" by A1,A3,XCMPLX_1:5;
  hence thesis by A4,XCMPLX_1:201;
end;
