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sci.math |
> > First I show for all f,g > > Hence immediately > > Consequently > > which shows > "f*(x) x g*(x) subset gf^-1" However, if you read my other recent post, you will see that I retracked f = { (n,m) in NxN | n <= m } ff^-1 = NxN = gf^-1 On Fri, 19 Sep 2008, Victor Porton wrote: The cross product
> On Sep 18, 11:58 am, William Elliot <ma...@hevanet.remove.com> wrote:
> > I have found an astonishingly simple and direct way of proving the major
> > lemma of that paper.
> > x in dom f /\ dom g ==> f*(x) x g*(x) subset gf^-1
> > x in dom f /\ dom g ==> f*(x) x g*(x) /\ gf^-1 = f*(x) x g*(x)
> > ff^-1 = gf^-1 ==> for all x in dom f /\ dom g, f*(x) = g*(x)
> > ff^-1 = gf^-1, dom f subset dom g ==> for all x in dom f, f*(x) = g*(x)
> > and finally
> > ff^-1 = gf^-1, dom f subset dom g ==> f <= g
> What you mean by "x"?
. . AxB = { (x,y) | x in A, y in B }
that proof. Is this a counter example to the lemma? N is positive
integers.
g = NxN; f subset g; dom f = dom g