¹Confusingly, it is also a common practice (dating back to Euclid) to use the word “proposition” synonymously with “theorem”. We will confine ourselves to the logician’s usage, according to which a proposition is a statement susceptible to proof, whereas a theorem (or “lemma” or “corollary”) is such a statement that has been proven. Thus “0 = 1” and its negation “¬(0 = 1)” are both propositions, but only the latter is a theorem.