FoundationsLesson 03 / 09

Check the evidence, not the author.

starts with a candidate that already exists. The asks whether every step follows the formal rules and whether the conclusion matches the goal.

Under assumptions Γ, proof term p proves proposition P.

1. Inspect the whole tree

The checker follows the recursively. It tracks the , checks the premises of each rule, and establishes the conclusion of each node.

For example, referring to an assumption that is not in scope must fail. A convincing label in the editor cannot fix that error.

2. Keep results honest

A checked result comes from actual kernel execution. A displayed example, valid JSON, or a successful TypeScript build is not a kernel verdict.

The playground starts with “Not checked”. Press Check proof to run the kernel and inspect the result. Changing examples clears the previous verdict.

3. Take this with you

finds candidate evidence. Checking validates supplied evidence. A failed search would not establish that no proof exists.

Reference: Proof checking. Validate every step.