| Some definitions of interest. |
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hanoi_seq | Def s is a Hanoi(n disk) seq on a..z
Def == x,x':{a...z}.
Def == x+1 = x'  ( k:{1...n}. Moving disk k of n takes s(x) to s(x')) |
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| Thm* n: , a,z: , s:({a...z} {1...n} Peg).
Thm* s is a Hanoi(n disk) seq on a..z Prop |
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hanoi_PEG | Def Peg == {1...3} |
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| Thm* Peg Type |
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hanoi_seq_deepen | Def (s(?) {to n} h {to n'})(x) == s(x) {to n} h {to n'} |
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| Thm* a,z: , n: , s:({a...z} {1...n} Peg), n': .
Thm* n n'
Thm* 
Thm* ( h:({n+1...n'} Peg). (s(?) {to n} h {to n'}) {a...z} {1...n'} Peg) |
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hanoi_seq_join | Def (s1 @(m) s2)(x) == if x m s1(x) else s2(x) fi |
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| Thm* n: , m,a,z: , s1:({a...m} {1...n} Peg), s2:({m+1...z} {1...n} Peg).
Thm* (s1 @(m) s2) {a...z} {1...n} Peg |
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int_iseg | Def {i...j} == {k: | i k & k j } |
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| Thm* i,j: . {i...j} Type |
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int_upper | Def {i...} == {j: | i j } |
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| Thm* n: . {n...} Type |
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member_and | Def x A, P == x A & P |
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nat_plus | Def  == {i: | 0<i } |
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| Thm*  Type |
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nequal | Def a b T == a = b T |
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| Thm* A:Type, x,y:A. (x y) Prop |