reserve a,b,c,d,x,j,k,l,m,n,o,xi,xj for Nat,
  p,q,t,z,u,v for Integer,
  a1,b1,c1,d1 for Complex;

theorem
  for b be non zero Nat holds a lcm ((n*a+1)*b) = (n*a+1)*(a lcm b)
  proof
    let b be non zero Nat;
    a lcm (a*(n*b) + b) = ((a*n)*b/b+1)*(a lcm b) by LCM2;
    hence thesis by XCMPLX_1:89;
  end;
