Keith Weber, a friend and researcher in mathematical practice, has asked me for instances where a mathematician has proved a theorem and then another mathematician reads the proof and sees the essence of it better than the original mathematician who wrote it.

I told him that I think this phenomenon occurs quite commonly --- it is the basis of many mathematical collaborations.

But he needs clear citable instances of the phenomenon from the literature (or MathOverflow). Can Math Twitter help out?

I expect that there must be some excellent instances of this on MathOverflow, where the timing of the contributions and exchanges is laid out clearly.

Can anyone provide links to clear instances of this phenomenon?

Keith himself had identified the Solovay-Tennenbaum proof of the consistency of Suslin's Hypothesis, and Martin's observation that it proved the consistency of Martin's Axiom.