Nuprl - Proof: nat prime div each factorLEMMA 1 1 1 2 1 1 1

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At: nat prime div each factorLEMMA 1 1 1 2 1 1 1

1. X :

2. prime(X)
3.

X1:

. X1<X

prime(X1)

(

a,b:

. X1 | a

X1 | a

X1 | b)
4. W :

W1:

. W1<W

0<W1

W1<X

(

. X | t

X | t)
6. 0<W
7. W<X
8. t :

9. u :

10. t

W = X

u
11.

W = 1
12. X1 : {2...}
13. X1

W
14. prime(X1)
15. c :

16. W = X1

c
17. t

c = X

X | t

By:	Inst: Hyp:3 Using:[X1 \| X \| u] ...a

Generated subgoals:

1   X1 | Xu
1 step

2 18. X1 | X  X1 | u
  X | t
10 steps

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