Nuprl - Proof: search property 2 1 2 2 2 1 1

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At: search property 2 1 2 2 2 1 1

1. k :

2. 0<k
3.

P:(

(k-1)

).
3. ((

i:

(k-1). P(i))

0<search(k-1;P))
3. & (0<search(k-1;P)
3. & (

3. & (P(search(k-1;P)-1) & (

j:

(k-1). j<search(k-1;P)-1

P(j)))
4. P :

k

5. (

i:

(k-1). P(i))

0<search(k-1;P)
6. (

i:

(k-1). P(i))

(0<search(k-1;P))
7. 0<search(k-1;P)
7.

7. P(search(k-1;P)-1) & (

j:

(k-1). j<search(k-1;P)-1

P(j))
8.

0<search(k-1;P)
9. i :

k
10. P(i)
11.

i<k-1

P(k-1)

By:	Subst' (i = k-1) -2

Generated subgoals:

None

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