reserve d,i,j,k,m,n,p,q,x,k1,k2 for Nat,
  a,c,i1,i2,i3,i5 for Integer;

theorem Th2:
  for p being Nat holds p is prime implies m,p are_coprime or m gcd p = p
proof
  let p be Nat;
A1: m gcd p divides p by NAT_D:def 5;
  assume p is prime;
  then m gcd p = 1 or m gcd p = p by A1,INT_2:def 4;
  hence thesis by INT_2:def 3;
end;
