| Rank | Theorem | Name | 
| 15 |  X:  . Thm* prime(X) Thm*    Thm* (  X1:  . X1<X   prime(X1)   (  a,b:  . X1 | a  b   X1 | a  X1 | b)) Thm*    Thm* (  W:  . 0<W   W<X   (  t:  . X | t  W   X | t)) | [nat_prime_div_each_factorLEMMA] | 
| cites the following: | ||
| 14 |  x:{2...}.  p:{2...}. p  x & prime(p) & p | x | [prime_or_smaller_prime_factor] | 
| 0 |  Q     P   Q | [disjunct_elim] | 
| 11 |  x:  . prime(x)   (  i:{2..x  }.  i | x) | [natprime_nondivs] | 
| 2 |  a,b:  . a | b   (  c:  . b = a  c) | [divides_def_on_nat] | 
| 4 |  a,b:  . 0<a  b   0<a & 0<b | [pos_mul_arg_boundsNat] | 
| 2 |  i:{2...}, j:{1...}. j<i  j | [factor_smaller] |