  We present new data structures for quasistrict higher categories, in which
associativity and unit laws hold strictly. Our approach has low axiomatic
complexity compared to traditional algebraic definitions of higher categories,
and we use it to give a practical definition of quasistrict 4-category. It is
also amenable to computer implementation, and we exploit this to give a new
machine-verified algebraic proof that every adjunction of 1-cells in a
quasistrict 4-category can be promoted to a coherent adjunction satisfying the
butterfly equations.
