= Solution
\b[The new bridge is made by an intramolecular <Michael addition>.] On the <cyclohexanone> side, the methyl-bearing fused alpha <carbon> is quaternary and cannot be deprotonated there. <triethylamine> can instead generate a small equilibrium population of the <enolate> at the other, methylene alpha <carbon>. Its <carbon> attacks the beta <carbon> of the <enone> in the seven-membered ring. The <enone> pi <electrons> move towards its <carbonyl> and then onto <oxygen>, creating the new bridge and a second <enolate>.
<protonation> of that <enolate> at the former methyl-substituted <enone> alpha <carbon> restores the left-hand <ketone>. The initial <enone> C=C has therefore become a saturated C–C bond while one new transannular C–C bond forms. Both <ketones> are retained, and the initial two-ring framework becomes a three-ring framework without changing the total <index of hydrogen deficiency>. The methyl originally at the fused quaternary centre does not migrate; the other methyl ends up on a protonated, formerly unsaturated <carbon>. A strong-<base (chemistry)> concentration large enough for quantitative <enolate> generation is unnecessary for a favourable intramolecular trapping reaction, and neither an aldol <dehydration> nor a methyl shift is needed.
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