Nuprl - Proof: hanoi general exists lemma2PROGworks 1 1 1 2

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At: hanoi general exists lemma2PROGworks 1 1 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)
16. i : {1...n-1}

(s1(?) {to n-1}

f {to n})(m,i)

(s1(?) {to n-1}

f {to n})(m,n)

& (s2(?) {to n-1}

g {to n})(m+1,i)

(s2(?) {to n-1}

g {to n})(m+1,n)

By:	m {a...m} Asserted THEN Guarding (<fun>(n)) Rewrite by Thm: hanoi seq deepen loweq THEN Rewrite by Thm: hanoi seq deepen higheq

Generated subgoals:

1 17. m  {a...m}
  s1(m,i)  f(n)
1 step

2 17. m  {a...m}
  s2(m+1,i)  g(n)
1 step

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IF YOU CAN SEE THIS go to /sfa/Nuprl/Shared/Xindentation_hack_doc.html

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