The possibility of carbon-carbon double bond formation within a ß-lactam ring
is suggested by the known tendency of penicillins with electron-withdrawing
substituents, such as phthalimido, at the 6-position to undergo base-promoted
rearrangement to thiazetinones,  a reaction for which the azetone 11
is reasonabily proposed as an intermediate. 
Moreover, a 3,4-unsaturaded ß-lactam has been detected spectroscopically, 
and azetinones fused to benzene or pyridine rings are well-known compounds.