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The question of whether two proofs are essentially the same is sometimes called "proof identity". It is an active topic in proof theory and there is an old MO thread with some references:

When are two proofs of the same theorem really different proofsWhen are two proofs of the same theorem really different proofs

The question of whether two proofs are essentially the same is sometimes called "proof identity". It is an active topic in proof theory and there is an old MO thread with some references:

When are two proofs of the same theorem really different proofs

The question of whether two proofs are essentially the same is sometimes called "proof identity". It is an active topic in proof theory and there is an old MO thread with some references:

When are two proofs of the same theorem really different proofs

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The question of whether two proofs are essentially the same is sometimes called "proof identity". It is an active topic in proof theory and there is an old MO thread with some references:

When are two proofs of the same theorem really different proofs