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

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At: sqrt prime irrational 1 1 1 2 1 1 1 2 1 1 1

1. p:
2. prime(p)
3. 0 < p
4. m:
5. m1:. m1 < m (n:. m1m1 = pnn n = 0)
6. n:
7. ((m p)p+(m mod p))((m p)p+(m mod p)) = pnn
8. n = 0
9. m = (m p)p+(m mod p)
10. (m mod p) < p
11. n@0:. nn = pn@0n@0 n@0 = 0
12. p | ((m mod p)(m mod p))
13. c:
14. (m mod p) = pc
15. c < 1
16. c < 0

n = 0

By: Assert (pc < 0)

Generated subgoals:

1 pc < 0 1 step

2 17. pc < 0
n = 0 Auto

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