ABSTRACT
The corresponding result for the co-cause is algebraically satisfying, but not generally causal:
bi=b,.2vb12x2 To demonstrate this, first note that every f in the definition of bj.2 is also in the definition of b\. Further, if f appears in the definition of b!2, then fx2€ TlFi and fx2hr* y imply that fx2 is in the definition of bi. This shows that bi > bi.2vbi2x2. Conversely, suppose that f is in the definition of bi. If feIIFi2, then f is in the definition of bi.2. Otherwise, i f f = gx2 with ge!IFi2 then either g is in the definition of bJ2 implying f < b!2x2, or else gxj ~s~^ y implying g in the definition of bj.2 because g'r* y. This shows that bi < bi.2vbi2x2, completing the demonstration.
