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

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At: search property 2 1 2 1 2 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.

(

i:

(k-1). P(i))
9.

0<search(k-1;P)
10. P(k-1)
11. 0<k

i:

k. P(i)

By:	InstConcl [k-1]

Generated subgoals:

None

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