Q:\CROSS\CROSS.TXT        

1999 July 29      (corrected 2000 August 6)

The function that takes pair(x,y) to cross(x,y) could be conveniently
defined as the composite of IMAGE(TWIST) and CART:

equal(composite(IMAGE(TWIST),CART),CROSS).

This depends on having a suitable formula for TWIST.  We do have such
a formula, obtained using the GOEDEL program:

equal(intersection(composite(inverse(FIRST),cross(FIRST,FIRST)), 
      composite(inverse(SECOND),cross(SECOND,SECOND))),TWIST).

This looks like a promising starting point for the theory of the
function CROSS.

2000 August 6

Now that we have developed the theory of TWIST, the theory of CROSS
should be feasible.