fzn_lex_less_set.mzn

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% Requires that the array 'x' is strictly lexicographically less than array 'y'.
% Compares them from first to last element, regardless of indices
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predicate fzn_lex_less_set(array[int] of var set of int: x,
                           array[int] of var set of int: y) =
    let { int: lx = min(index_set(x)),
          int: ux = max(index_set(x)),
          int: ly = min(index_set(y)),
          int: uy = max(index_set(y)),
          int: size = max(ux - lx, uy - ly),
          array[0..size+1] of var bool: b }
    in
    b[0]
    /\
    forall(i in 0..size) (
        b[i] = ( x[lx + i] <= y[ly + i]
                 /\
                (x[lx + i] <  y[ly + i] \/ b[i+1]) )
    )
    /\
    b[size + 1] = (ux - lx < uy - ly);

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