FoundationsLesson 01 / 09
A statement is not a proof.
A is what you want to establish. A is the evidence that establishes it. Keeping them separate is the first step to understanding a proof assistant.
1. The statement
The letter stands for a proposition. The above is another proposition: it says that evidence for A is enough to obtain evidence for A.
Writing the statement tells us the goal. It does not tell the prover why that goal follows.
2. The evidence
Informally, assume we have evidence for A, then return the same evidence. That is the idea of the identity proof.
A formal version must record these steps in a . The will check the tree before accepting it.
3. Take this with you
A goal asks a question. A candidate proof proposes an answer. decides whether the evidence follows the rules.