is mentioned by
Thm* p q Thm* Thm* (a:, z:{a...}, s:({a...z}{1...n}Peg). Thm* (s is a Hanoi(n disk) seq on a..z & s(a) = (i.p) & s(z) = (i.q) Thm* ( Thm* ((x:{a...z-1}, y:{x+1...z}, p',q':Peg. Thm* (((u:{a...x}. s(u,n) = p) & (u:{y...z}. s(u,n) = q) Thm* ((& s(x) = (i.p') {1...n-1}Peg & s(y) = (i.q') {1...n-1}Peg Thm* ((& p p' Thm* ((& q q')) | [hanoi_sol2_analemma] |
[exponentiation_wf_nat_plus] | |
Thm* p q Thm* Thm* (a:. Thm* (HanoiSTD(n disks; from: p; to: q; indexing from: a) Thm* (= Thm* ((HanoiSTD(n-1 disks; from: p; to: otherPeg(p; q); indexing from: a)/m,s1. Thm* ((HanoiSTD(n-1 disks; from: otherPeg(p; q); to: q; indexing from: m+1) Thm* ((/z,s2. <z,HanoiHelper(n; s1; i.p; s2; i.q)/r1,r2. r1 @(m) r2>)) | [hanoi_sol2_ala_generalPROGcomp] |
Thm* f(n) g(n) Thm* Thm* (s1:({a...m}{1...n-1}Peg), s2:({m+1...z}{1...n-1}Peg). Thm* (s1 is a Hanoi(n-1 disk) seq on a..m Thm* (& s1(a) = f {1...n-1}Peg Thm* (& s2 is a Hanoi(n-1 disk) seq on m+1..z Thm* (& s2(z) = g {1...n-1}Peg Thm* (& s1(m) = s2(m+1) Thm* (& (i:{1...n-1}. s1(m,i) f(n) & s2(m+1,i) g(n)) Thm* ( Thm* ((HanoiHelper(n; s1; f; s2; g)/r1,r2. Thm* (((r1 @(m) r2) is a Hanoi(n disk) seq on a..z & r1(a) = f & r2(z) = g)) | [hanoi_general_exists_lemma2PROGworks] |
Thm* s1:({a...m}{1...n-1}Peg), s2:({m+1...z}{1...n-1}Peg). Thm* HanoiHelper(n; s1; f; s2; g) Thm* ({a...m}{1...n}Peg)({m+1...z}{1...n}Peg) | [hanoi_general_exists_lemma2PROG_wf] |
Thm* f(n) g(n) Thm* Thm* (s1:({a...m}{1...n-1}Peg), s2:({m+1...z}{1...n-1}Peg). Thm* (s1 is a Hanoi(n-1 disk) seq on a..m Thm* (& s1(a) = f {1...n-1}Peg Thm* (& s2 is a Hanoi(n-1 disk) seq on m+1..z Thm* (& s2(z) = g {1...n-1}Peg Thm* (& s1(m) = s2(m+1) Thm* (& (i:{1...n-1}. s1(m,i) f(n) & s2(m+1,i) g(n))) Thm* Thm* (r1:({a...m}{1...n}Peg), r2:({m+1...z}{1...n}Peg). Thm* ((r1 @(m) r2) is a Hanoi(n disk) seq on a..z & r1(a) = f & r2(z) = g) | [hanoi_general_exists_lemma2] |
Thm* f(n) = g(n) Thm* Thm* (a:, z:{a...}. Thm* ((s:({a...z}{1...n-1}Peg). Thm* ((s is a Hanoi(n-1 disk) seq on a..z Thm* ((& s(a) = f {1...n-1}Peg Thm* ((& s(z) = g {1...n-1}Peg) Thm* ( Thm* ((s:({a...z}{1...n}Peg). Thm* ((s is a Hanoi(n disk) seq on a..z & s(a) = f & s(z) = g)) | [hanoi_general_exists_lemma1] |
In prior sections: int 1 int 2
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