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

theorem
  for i being Nat holds i,i+1 are_coprime
proof
  let k be Nat;
  k gcd (k+1) = (1+k*1) gcd k .= 1 gcd k by EULER_1:8
    .= 1 by NEWTON:51;
  hence thesis by INT_2:def 3;
end;
