The impact of proof steps sequence on proof readability - experimental setting

Different sequences of proof steps may result in different experiences of the overall formal proof clarity. There is a conjecture that sequence in which more steps refer to the content of the preceding statement (1) is more comprehensible than the one in which references span longer distances (2). We studied the claim in experimental setting where subjects indicated their reading preference with two versions of the same proof. The difference between their reports indicates that contrary to the conjecture, proofs of the kind (2) can give cognitive advantage in a statistically significant way.