The cycloaddition of (Z)-7-(prop-1-enyl)-7-azabicyclo[4.1.0]heptane with dimethyl acetylene dicarboxylate (DMAD) was reported previously to proceed with complete stereoselectivity. Quantum chemical calculations (B3LYP) were used to evaluate the mechanism of the cyclization process, and it was discovered that a stepwise pathway is preferred. The subsequent electrocyclic ring opening reaction of the cyclobutene was also studied, and it was found that ring opening to the "methyl-in" dienamine is preferred to the "methyl-out" product by some 4-5 kcal/mol.