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hanoi general exists lemma2PROGworks13 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)
(s2(?) {to n-1} g {to n})(z) = g