 Another early problem in the \(\lambda\)-calculus was whether it is consistent at all. In this context, inconsistency means that all terms are equal: one can reduce any \(\lambda\)-term \(M\) to any other \(\lambda\)-term \(N\). That this is not the case is an early result of \(\lambda\)-calculus. Initially one had results showing that certain terms were not interconvertible (e.g., \(\mathbf{K}\) and \(\bS)\); later, a much more powerful result, the so-called Church-Rosser theorem, helped shed more light on \(\beta\)-conversion and could be used to give quick proofs of the non-inter-convertibility of whole classes of \(\lambda\)-terms. See below for more detailed discussion of consistency.