A proof tactic automates a recognizable reasoning step such as simplifying an expression, applying a theorem, splitting cases or invoking a decision procedure. Users combine tactics to move from an initial theorem statement to goals that the system can close.
Tactic search can explore many possible proof paths, which makes it suitable for automation and learned guidance. Successful execution is not trusted by itself. The resulting proof term must still pass the proof assistant's kernel.
ELI5
A proof tactic is a reusable method that helps solve part of a formal proof. It can simplify an expression, apply a known theorem, split a problem into cases, or turn one difficult goal into several easier goals.
For example, a tactic might automatically replace equal expressions and remove obvious arithmetic steps. The tactic is a helper, not the final authority, because the proof assistant still checks the complete proof evidence it produces.
Do proof tactics prove the theorem directly?
They guide and automate proof construction, but the proof assistant accepts the theorem only after its kernel validates the produced proof term.
Can AI choose proof tactics?
Yes. A model can propose or rank tactics based on the current goal and prior proofs, helping search a large space of possible steps.
