include "../std/fzn_lex_less_bool_reif.mzn";

predicate fzn_lex_less_bool_imp(array[int] of var bool: x,
                                array[int] of var bool: y,
                                var bool: c) =
    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
    (c -> 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);