 As to the Diagonalization Lemma, actually Gödel himself originally demonstrated only a special case of it, that is, only for the provability predicate. The general lemma was apparently first discovered by Carnap 1934 (see Gödel 1934, 1935). Still more general versions, for formulas with free variables, were presented in Ehrenfeucht &amp; Feferman 1960 and Montague 1962 (see Smoryński 1981).