A Proof is not a statement. A theorem is a statement. Proofs are usually not completely formal or even formalizable. Math is not completely well founded. "Unr

A Proof is not a statement. A theorem is a statement. Proofs are usually not completely formal or even formalizable. Math is not completely well founded. "Unravelling it all the way" might be an open research project, or a new conjecture directly inspired by the second, apparently different proof. Showing these two profs to be equivalent might depend on a major new idea that happens after the two proofs are createdm This is hinted at in the OP discussion of Terry Tao.