Nuprl - Proof: iter prod zero iff factor zero 1 1 1 2 1

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At: iter prod zero iff factor zero 1 1 1 2 1

1. a :

2. k :

3. 0<k
4.

b:

, e:({a..b

}

).
4. b-a = k-1

((

i:{a..b

}. e(i)) = 0

(Or i:{a..b

}. e(i) = 0))
5. b :

6. e : {a..b

}

7. b-a = k

(

i:{a..b-1

}. e(i))

e(b-1) = 0

(Or i:{a..b-1

}. e(i) = 0)

e(b-1) = 0

By:	Rewrite by Thm* a,b:. ab = 0 a = 0 b = 0

Generated subgoal:

1   ( i:{a..b-1}. e(i)) = 0  e(b-1) = 0

  (Or i:{a..b-1}. e(i) = 0)  e(b-1) = 0
1 step

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(13steps total) PrintForm Definitions Lemmas IteratedBinops Sections DiscrMathExt Doc