Re: struggling proving lattice identity

From: Ken Pledger (Ken.Pledger_at_mcs.vuw.ac.nz)
Date: 02/23/05 

Date: Wed, 23 Feb 2005 16:34:50 +1300

In article <1109126939.328733.226210@g14g2000cwa.googlegroups.com>,
 mikharakiri_nospaum@yahoo.com wrote:

> a >= c --> a/\(b\/c) >= (a/\b)\/c
>
> Assuming that algebraic manipulations with equalities are easier, let's
> rewrite it as:
>
> a/\c=c --> a/\(b\/c)/\((a/\b)\/c) = (a/\b)\/c
>
> and here I'm effectively stuck. I'm unable see how to rearrange terms
> and apply lattice axioms.

      This is the modular inequality, and it's usually proved by using
the partial ordering. Look at the two terms on the L.H.S. separately,
and show that a >= R.H.S. and b\/c >= R.H.S. Alternatively, look at
the R.H.S. terms a/\b and c separately, and show that each <= L.H.S.

            Ken Pledger.