
theorem lem24nat:
  for n being natural number st n divides 24 holds
    n=1 or n=2 or n=3 or n=4 or n=6 or n=8 or n=12 or n=24
proof
  let n be natural number;
  assume n: n divides 24;
  then n <= 24 by INT_2:27;
  then el: n=0 or...or n=24;
  n0: not 0 divides 24 by INT_2:3;
  5*4 < 24 < 5*(4+1); then
  n5: not 5 divides 24 by NEWTON03:40;
  7*3 < 24 < 7*(3+1); then
  n7: not 7 divides 24 by NEWTON03:40;
  9*2 < 24 < 9*(2+1); then
  n9: not 9 divides 24 by NEWTON03:40;
  10*2 < 24 < 10*(2+1); then
  n10: not 10 divides 24 by NEWTON03:40;
  11*2 < 24 < 11*(2+1); then
  n11: not 11 divides 24 by NEWTON03:40;
  13*1 < 24 < 13*(1+1); then
  n13: not 13 divides 24 by NEWTON03:40;
  14*1 < 24 < 14*(1+1); then
  n14: not 14 divides 24 by NEWTON03:40;
  15*1 < 24 < 15*(1+1); then
  n15: not 15 divides 24 by NEWTON03:40;
  16*1 < 24 < 16*(1+1); then
  n16: not 16 divides 24 by NEWTON03:40;
  17*1 < 24 < 17*(1+1); then
  n17: not 17 divides 24 by NEWTON03:40;
  18*1 < 24 < 18*(1+1); then
  n18: not 18 divides 24 by NEWTON03:40;
  19*1 < 24 < 19*(1+1); then
  n19: not 19 divides 24 by NEWTON03:40;
  20*1 < 24 < 20*(1+1); then
  n20: not 20 divides 24 by NEWTON03:40;
  21*1 < 24 < 21*(1+1); then
  n21: not 21 divides 24 by NEWTON03:40;
  22*1 < 24 < 22*(1+1); then
  n22: not 22 divides 24 by NEWTON03:40;
  23*1 < 24 < 23*(1+1); then
  not 23 divides 24 by NEWTON03:40;
  hence n=1 or n=2 or n=3 or n=4 or n=6 or n=8 or n=12 or n=24
  by n,el,n0,n5,n7,n9,n10,n11,n13,n14,n15,n16,n17,n18,n19,n20,n21,n22;
end;
