/**
* Returns the conjecture proposition_2_14_1.
*
* @return proposition_2_14_1
*/
public final Formula proposition2141() {
// all c1, c2: curve, p: point |
// p->c1->c2 in meet && c1->c2 in sum.open =>
// all q: point - p | c1 + c2 !in q.incident
final Variable c1 = Variable.unary("C1");
final Variable c2 = Variable.unary("C2");
final Variable p = Variable.unary("P");
final Variable q = Variable.unary("Q");
final Expression e0 = c1.product(c2);
final Formula f0 = p.product(e0).in(meet).and(e0.in(sum.join(open)));
final Formula f1 = c1.union(c2).in(q.join(incident)).not().forAll(q.oneOf(point.difference(p)));
return f0.implies(f1).forAll(c1.oneOf(curve).and(c2.oneOf(curve)).and(p.oneOf(point)));
}
/**
* Helper method that returns the constraint that the sig has exactly "n" elements, or at most "n"
* elements
*/
private Formula size(Sig sig, int n, boolean exact) {
Expression a = sol.a2k(sig);
if (n <= 0) return a.no();
if (n == 1) return exact ? a.one() : a.lone();
Formula f = exact ? Formula.TRUE : null;
Decls d = null;
Expression sum = null;
while (n > 0) {
n--;
Variable v = Variable.unary("");
kodkod.ast.Decl dd = v.oneOf(a);
if (d == null) d = dd;
else d = dd.and(d);
if (sum == null) sum = v;
else {
if (f != null) f = v.intersection(sum).no().and(f);
sum = v.union(sum);
}
}
if (f != null) return sum.eq(a).and(f).forSome(d);
else return a.no().or(sum.eq(a).forSome(d));
}