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(* 02110-1301 USA                                                     *)
(** modprime. Some nice lemmas about div, mult, mod, prime, and gcd.  @author Olga Caprotti and Martijn Oostdijk @version $Revision$ *)
(** This lemma simply states that: if a divides b where 0<a<b, then there is a prime factor qi of b such that a divides (b/qi). I.e. If you divide by a non-trivial divisor, then the other divisor contains a prime factor. *)

Lemma techlemma3 :
forall (qlist : natlist) (a b : nat),
0 < a ->
a < b ->
Divides a b ->
b = product qlist ->
allPrime qlist ->
exists qi : nat, inlist nat qi qlist /\ Divides a (multDrop qi qlist).