Lean 4 is uses constructive logic. If a closed world assumption requires that a statement that is true is also known to be true, and that any statement that is not known to be true is therefore false, that is not true of constructive systems. I only use Rocq, but I believe the type theories in Rocq and Lean 4 are basically similar variations on the Calculus of Constructions in both cases, though there are important differences. In a constructive theory something is true if a proof can be constructed, but the lack of a proof does not entail that something is false. One needs to prove that something is false. In constructive type theory, one can say, that something is true or false.