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Characterization of legitimate moves in the Towers of Hanoi.

Stacking situations f and g differ just about where disk k is, and none of the disks smaller than k is in the way.

Who Cites hanoi step at?
hanoi_step_atDef  Moving disk k of n takes f to g
Def  == (i:{1...n}. f(i) = g(i Peg  i  k)
Def  == & (i:{1...k-1}. f(i f(k Peg & g(i g(k Peg)
Thm*  n:f,g:({1...n}Peg), k:{1...n}.
Thm*  Moving disk k of n takes f to g  Prop
hanoi_PEGDef  Peg == {1...3}
Thm*  Peg  Type
nequalDef  a  b  T == a = b  T
Thm*  A:Type, x,y:A. (x  y Prop
int_isegDef  {i...j} == {k:ik & kj }
Thm*  i,j:. {i...j Type
iffDef  P  Q == (P  Q) & (P  Q)
Thm*  A,B:Prop. (A  B Prop
leDef  AB == B<A
Thm*  i,j:. (ij Prop
notDef  A == A  False
Thm*  A:Prop. (A Prop
rev_impliesDef  P  Q == Q  P
Thm*  A,B:Prop. (A  B Prop

Syntax:Moving disk k of n takes f to g has structure: hanoi_step_at(nfgk)

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