EDIT: As the question hasn't attracted any answers, I tried to put in more detail.
Gibbs's phase rule for a 2 component system at constant pressure says that $F=3-P$, i.e., that the number of degrees of freedom is three minus the number of phases present. This should mean that when $P=3$, there should be no degrees of freedom and three phases should only be in equilibrium at a single point.
However, looking at the eutectic phase diagram, this seems not to be true. Even visually - four lines intersect at the eutectic point, not three.
And my understanding is that the three phases, $\alpha$, $\beta$ and $L$ can be in equilibrium along a line at the eutectic temperature, not only at a single point.
This can be seen by looking at the Gibbs free energy of the three phases at the eutectic temperature, which should look like this:
By the common tangent construction, the three phases are at equilibrium along a range of compositions, and thus $F=1$, not $0$.
Is there a mistake in my understanding, or is it a 'violation' of the phase rule?