The syllogism corresponding to the above type of argument would go as follows.

**Fact B.2***
If < whatever hypothesis >, then ab = bc.
*

**Fact B.3***
If a, b and c are matrices, no eigenvalue of a is an eigenvalue of c
and ab = bc, then b = 0.
*

**Fact B.4***
If < whatever hypothsis > and b = 0, then < desired
conclusion >.
*

**Conclusion B.5***
If < whatever hypothesis >, then < desired conclusion
>.
*

Fact B.2 would be seen by using the algorithms in this paper. Fact B.3 is an observation from analysis. Fact B.4 would be seen by using the algorithms in this paper. Conclusion B.5 is a tautological conclusion of the Facts B.2, B.3 and B.4.

Wed Jul 3 10:27:42 PDT 1996