reserve x,y,z for Real,
  a,b,c,d,e,f,g,h for Nat,
  k,l,m,n,m1,n1,m2,n2 for Integer,
  q for Rational;

theorem Th8:
  0 gcd m = |.m.| & 1 gcd m = 1
proof
A1: m gcd 1=|.m.| gcd |.1.| by INT_2:34
    .=|.m.| gcd 1 by ABSVALUE:def 1
    .=1 by NEWTON:51;
  m gcd 0=|.m.| gcd |.0 qua Nat.| by INT_2:34
    .=|.m.| gcd 0 by ABSVALUE:2
    .=|.m.| by NEWTON:52;
  hence thesis by A1;
end;
