Writing proofs — Coq 8.12.0 documentation

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# Writing proofs

Coq is an interactive theorem prover, or proof assistant, which means that proofs can be constructed interactively through a dialog between the user and the assistant. The building blocks for this dialog are tactics which the user will use to represent steps in the proof of a theorem.

Incomplete proofs have one or more open (unproven) sub-goals. Each goal has its own context (a set of assumptions that can be used to prove the goal). Tactics can transform goals and contexts. Internally, the incomplete proof is represented as a partial proof term, with holes for the unproven sub-goals.

When a proof is complete, the user leaves the proof mode and defers the verification of the resulting proof term to the kernel.

This chapter is divided in several parts, describing the basic ideas of the proof mode (during which tactics can be used), and several flavors of tactics, including the SSReflect proof language.

- Proof handling
- Tactics
- The SSReflect proof language
- Detailed examples of tactics
- Proof schemes

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