Nuprl - Proof: sqrt prime irrational 1 1 1 1 1 2

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At: sqrt prime irrational 1 1 1 1 1 2

1. p:
2. prime(p)
3. 0 < p
4. m:
5. m1:. m1 < m (n:. m1m1 = pnn n = 0)
6. n:
7. mm = pnn
8. n = 0
9. m = (m p)p+(m mod p)
10. (m mod p) < p
11. mn
12. 0 < nn

n < m

By: Inst Thm* a,b:, n:. ab nanb [m;n;n] THEN Inst Thm* a,b:, n:. ab nanb [m;n;m] THEN Inst Thm* a,b:. ab = ba [m;n]

Generated subgoal:

1 13. nmnn
14. mmmn
15. mn = nm
n < m 6 steps

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(42steps total) PrintForm Definitions Lemmas graph 1 2 Sections Graphs Doc