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prime factorization unique11 1. a : {2...}
2. b : 3. k : 4. k1:.
4. k1<k 4. 4. (g,h:({a..b}).
4. (is_prime_factorization(a; b; g) & is_prime_factorization(a; b; h)
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(a; b; g)
8. is_prime_factorization(a; b; h)
9. {a..b}(g) = k 10. {a..b}(g) = {a..b}(h)
11. j:{a..b}. 0<g(j)
g = h
By:
Analyze-1
THEN
Hyp:7
Thm*a,b:, f:({a..b}), j:{a..b}. 0<f(j) j | {a..b}(f)
Hyp:10
Thm*a:, b:, f:({a..b}), p:.
Thm* is_prime_factorization(a; b; f)
Thm* Thm* prime(p) p | {a..b}(f) p {a..b} & 0<f(p)