  We define dual equivalence for any collection of combinatorial objects
endowed with a descent set, and we show that giving a dual equivalence
establishes the symmetry and Schur positivity of the quasi-symmetric generating
function. We give an explicit formula for the Schur expansion of the generating
function in terms of distinguished elements of the dual equivalence classes.
These concepts and proofs simplify in the ubiquitous case when the collection
of objects has a sufficiently nice reading word.
