proof of modular law

First we show C+(BA)B(C+A):
Note that CB,BAB, and therefore C+(BA)B.
Further, CC+A, BAC+A, thus C+(BA)C+A.

Next we show B(C+A)C+(BA):
Let bB(C+A). Then b=c+a for some cC and aA. Hence a=b-c, and so aB since bB and cCB.
Hence aBA, so b=c+aC+(BA).

Title proof of modular law
Canonical name ProofOfModularLaw
Date of creation 2013-03-22 12:50:45
Last modified on 2013-03-22 12:50:45
Owner yark (2760)
Last modified by yark (2760)
Numerical id 8
Author yark (2760)
Entry type Proof
Classification msc 16D10
Related topic FirstIsomorphismTheorem