...but then again (1) nobody has ever seen an idealized perfectly competitive market; (2) it's by no means clear that an idealized perfectly competitive market even serves as a useful approximation to the ones we have; (3) efficiency (in the narrow sense defined by efficient markets) is not the goal we want to be pursuing anyway.
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There's a proof...
...but then again (1) nobody has ever seen an idealized perfectly competitive market; (2) it's by no means clear that an idealized perfectly competitive market even serves as a useful approximation to the ones we have; (3) efficiency (in the narrow sense defined by efficient markets) is not the goal we want to be pursuing anyway.