What is Proof assistant vs SMT-based verifier? Definition and why it matters
============================================================================

A proof assistant (Lean, Rocq, Isabelle, F*) checks human- or AI-written proofs against a small kernel and can express arbitrary mathematics; an SMT-based verifier (Picus, CIVER, Certora Prover, Kani) discharges properties automatically but only within decidable fragments and may return 'unknown'.

Detail: The practical trade: SMT tools give results in minutes with no proof engineering and no specification (for determinism) but time out on large or nonlinear problems; proof assistants scale to any property and any size at the cost of expert time. Mature pipelines use both: automatic checks first, proofs for what matters most.

Source page: https://sorryfree.com/glossary/proof-assistant-vs-smt/
Compiled by: sorryfree editors (https://sorryfree.com/about/)
Last reviewed: 2026-09-13