Nuprl - Proof: hanoi general exists lemma2PROGworks 1 2

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At: hanoi general exists lemma2PROGworks 1 2

1. n :

2. a :

3. z : {a...}
4. m : {a...z-1}
5. f : {1...n}

Peg
6. g : {1...n}

Peg
7. f(n)

g(n)
8. s1 : {a...m}

{1...n-1}

Peg
9. s2 : {m+1...z}

{1...n-1}

Peg
10. s1 is a Hanoi(n-1 disk) seq on a..m
11. s1(a) = f
12. s2 is a Hanoi(n-1 disk) seq on m+1..z
13. s2(z) = g
14. s1(m) = s2(m+1)
15.

i:{1...n-1}. s1(m,i)

f(n) & s2(m+1,i)

g(n)

(s1(?) {to n-1}

f {to n})(a) = f

By:	FunExtensionality THEN Decide: x<n

Generated subgoals:

1 16. x : {1...n}
17. x<n
(s1(?) {to n-1} f {to n})(a,x) = f(x)
2 steps

2 16. x : {1...n}
17. x<n
(s1(?) {to n-1} f {to n})(a,x) = f(x)
1 step

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(26steps total) Remark PrintForm Definitions Lemmas HanoiTowers Sections NuprlLIB Doc