In the community of the theorem prover Coq, a proof obtained by running a proven correct decision procedure is called a "proof by reflection". There is also th

In the community of the theorem prover Coq, a proof obtained by running a proven correct decision procedure is called a "proof by reflection". There is also the "proof by certificate" approach. You generate a potentially large proof certificate by an unverified program. Then you run a proven correct (small) checker on the certificate to concude that the theorem is correct.