reserve a,b,c,d,m,x,n,j,k,l for Nat,
  t,u,v,z for Integer,
  f,F for FinSequence of NAT;
reserve p,q,r,s for real number;

theorem Th8:
  a > b & a,b are_coprime implies (a+b) gcd (a-b) <= 2
  proof
    assume
    A1: a > b & a,b are_coprime; then
    consider c such that
    A2: a = b + c by NAT_1:10;
    c+1*b,b are_coprime by A1,A2; then
    c,b are_coprime by Th5; then
    2*b + c gcd c <= 2 by Lm5;
    hence thesis by A2;
  end;
