Constraint propagation using Projection rule I've found this example of constraint propagation using projection rule 


We have

C = { x1 ≠ x2, x1 ≥ x2 }

&lt; C; x1 ∈ {1,2,3}, x2 ∈ {1,2,3} &gt;


They say that applying propagation rule, does not give any simplification.

I'm not sure why this is the case. Shouldn't we get?

&lt; C; x1 ∈ {2,3}, x2 ∈ {1,2} &gt;


Other steps in the example, make sense that to me, e.g.

&lt; C; x1 ∈ {2}, x2 ∈ {1,2,3} &gt;


produces

&lt; C; x1 ∈ {2}, x2 ∈ {1} &gt;
You apply the propagation rule to a single constraint. 

The rules are defined in such a way that they can be applied efficiently. 
Otherwise, by applying the "generalized propagation rule" you could declare that a SAT instance is unsatisfiable in a single step.