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Example: Sorting Problem

• Input:
  • n in N ...the length of the sequence,
  • s: N_n -> R ...a sequence of length n on R.
• Output: t: N_n -> R such that
  • t is permutation of s,
  • t is sorted with respect to <= .

  t is permutation of s : <=>

  let n = length(t):

  n = length(s) /\

  exists p: p is permutation of length n /\  p o s = t;

  t is sorted with respect to <= : <=>

  forall 0 <= i < length(t)-1: ti <= ti+1.