
If the cyclobutane ring was to adopt a planar conformation, then in
the cis-isomer, the two substituents would be on the same face of
the ring and there would be a steric repulsion between them. In the trans-isomer
however, the two substituents will be on opposite faces of the four-membered
ring and there will be no interaction between them as shown below. Thus,
in this case the trans-isomer would be thermodynamically more stable.

The reaction occurs because the hydrogen atom next to the carbonyl of
the ester (in both the starting material and product) is acidic and can
be removed by a base such as sodium methoxide. This generates an enolate
which can be reprotonated from either face to either regenerate the starting
material or give the product. The product is the thermodynamically more
stable isomer, so eventually the trans-isomer (starting material)
is converted into the cis-isomer (product).

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