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At: prime factorization unique 1 1 1

1. a : {2...}
2. b : 
3. k : 
4. k1:
4. k1<k
4. 
4. (g,h:({a..b}).
4. (is_prime_factorization(abg) & is_prime_factorization(abh)
4. (
4. ({a..b}(g) = k1  {a..b}(g) = {a..b}(h g = h)
5. g : {a..b}
6. h : {a..b}
7. is_prime_factorization(abg)
8. is_prime_factorization(abh)
9. {a..b}(g) = k
10. {a..b}(g) = {a..b}(h)
11. j : {a..b}
12. 0<g(j)
13. prime(j)
14. j | {a..b}(g)
15. j | {a..b}(h)
16. 0<h(j)
  g = h


By: Thm*  a:b:f:({a..b}), p:.
Thm*  is_prime_factorization(abf)
Thm*  
Thm*  prime(p)
Thm*  
Thm*  p | {a..b}(f {a..b}(f) = p{a..b}(reduce_factorization(fp))


Generated subgoal:

1 17. j{a..b}(reduce_factorization(gj))
17. =
17. j{a..b}(reduce_factorization(hj))
  g = h

6 steps

About:
intnatural_numbermultiplyless_thanapplyfunctionequalimpliesandall
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(15steps total) PrintForm Definitions Lemmas FTA Sections DiscrMathExt Doc