File: even.mona

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var2 P,Q;
P\Q = {0,4} union {1,2}; # the formula from Section 1

var1 x;
var0 A;

ex2 Q: x in Q
  & (all1 q: 
      (0 < q & q <= x) =>
          (q in Q => q - 1 notin Q)
        & (q notin Q => q - 1 in Q))
  & 0 in Q;

A & x notin P;