Nuprl - Proof: prime divs mul via intseg 1 1 1 2 1

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At: prime divs mul via intseg 1 1 1 2 1

1. p :

2. prime(p)
3. a :

4. k :

5.

k1:

.
5. k1<k
5.

5. (

b:

.
5. (b-a = k1
5. (

5. ((

e:({a..b

}

). a<b

p | (

i:{a..b

}. e(i))

(

i:{a..b

}. p | e(i))))
6. b :

7. b-a = k
8. e : {a..b

}

9. a<b
10. p | (

i:{a..b

}. e(i))
11.

a+1 = b
12. p | (

i:{a..b-1

}. e(i))

e(b-1)

i:{a..b

}. p | e(i)

By:	FwdThru: Thm* X:. prime(X) (a,b:. X \| ab X \| a X \| b) on [ Hyp:-1 ] ... THEN Analyze-1

Generated subgoals:

1 13. p | ( i:{a..b-1}. e(i))
i:{a..b}. p | e(i)
2 steps

2 13. p | e(b-1)
i:{a..b}. p | e(i)
1 step

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