Editing Gödel's incompleteness theorems (section)

=== Computer verified proofs ===
{{See also|Automated theorem proving}}

The incompleteness theorems are among a relatively small number of nontrivial theorems that have been transformed into formalized theorems that can be completely verified by [[proof assistant]] software. Gödel's original proofs of the incompleteness theorems, like most mathematical proofs, were written in [[natural language]] intended for human readers.

Computer-verified proofs of versions of the first incompleteness theorem were announced by [[Natarajan Shankar]] in 1986 using [[Nqthm]] {{harv|Shankar|1994}}, by Russell O'Connor in 2003 using [[Rocq (software)|Rocq]] (previously known as ''Coq'') {{harv|O'Connor|2005}} and by John Harrison in 2009 using [[HOL Light]] {{harv|Harrison|2009}}. A computer-verified proof of both incompleteness theorems was announced by [[Lawrence Paulson]] in 2013 using [[Isabelle theorem prover|Isabelle]] {{harv|Paulson|2014}}.