reserve a,b,i,k,m,n for Nat;
reserve s,z for non zero Nat;
reserve r for Real;
reserve c for Complex;
reserve e1,e2,e3,e4,e5 for ExtReal;

theorem
  for a,b being Integer st a <> b holds
  {n where n is Nat: a+n,b+n are_coprime} is infinite
  proof
    let a,b be Integer;
    assume a <> b;
    then a < b or b < a by XXREAL_0:1;
    hence thesis by Lm39;
  end;
