Proofs in computability theory often invoke the Church–Turing thesis in an informal way to establish the computability of functions while avoiding the (often very long) details which would be involved in a rigorous, formal proof.[2] To establish that a function is computable by Turing machine, it is usually considered sufficient to give an informal English description of how the function can be effectively computed, and then conclude "by the Church–Turing thesis" that the function is Turing computable (equivalently, partial recursive).