# Forwards vs Backwards Proofs

• Backwards proof is using the rules backwards

• Given the rule:

$$\begin{prooftree} \AxiomC{$$\vdash S_1 \quad \dots \quad \vdash S_n$$} \UnaryInfC{$$\vdash S$$} \end{prooftree}$$

• Forwards proof:
• If we have proved $$\vdash S_1 \dots \vdash S_n$$, we can deduce $$\vdash S$$
• Backwards proof:
• To prove $$\vdash S$$, it is sufficient to prove $$\vdash S_1 \dots S_n$$