Lean's undated documentation (retrieved 2026-11-08) describes a formal mathematical statement, called a proposition, and a proof object: a precise expression representing a proof of that statement. The checker tests whether the object obeys the formal rules and matches the statement it is supposed to prove. This explains 'well-formed' and 'has the correct type' in this setting. The guarantee is relative to the formal statement and its assumptions. People still need to ask whether that statement captures the intended claim, whether its assumptions are appropriate and why the result matters. A checked proof is neither an empirical experiment nor a demonstration of human comprehension.

Evidence status: established_technical_distinction.