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hanoi sol2 via permshift21321131 1. n : 2. 0<n 3. p,q:Peg.
3. pq 3. 3. (z:{1...}, s:({1...z}{1...n-1}Peg).
3. (s is a Hanoi(n-1 disk) seq on 1..z & s(1) = (i.p) & s(z) = (i.q))
4. p : Peg
5. q : Peg
6. pq 7. p otherPeg(p; q)
8. otherPeg(p; q) q 9. m : {1...}
10. s1 : {1...m}{1...n-1}Peg
11. s1 is a Hanoi(n-1 disk) seq on 1..m 12. s1(1) = (i.p)
13. s1(m) = (i.otherPeg(p; q))
14. (x,i. permute(p to otherPeg(p; q) ; otherPeg(p; q) to q)(s1(x,i)))
14. is a Hanoi(n-1 disk) seq on 1..m 15. (x,i. permute(p to otherPeg(p; q) ; otherPeg(p; q) to q)(s1(x-m,i)))
15. is a Hanoi(n-1 disk) seq on 1+m..m+m (i.otherPeg(p; q))
=
(i.permute(p to otherPeg(p; q) ; otherPeg(p; q) to q)(p))
{1...n-1}Peg
By:
Analyze
THEN
Rewrite by Thm*p,r,q,s:Peg. pqrs permute(p to r ; q to s)(p) = r
Generated subgoals:
None
About:
IF YOU CAN SEE THIS go to /sfa/Nuprl/Shared/Xindentation_hack_doc.html