
# 2.8: Summary


## Summary

• A “two-column proof” is a tool that we use to learn techniques for writing proofs.
• The left-hand column contains a sequence of assertions.
• The right-hand column contains a justification for each assertion.
• Each row of the proof is numbered (in the left margin) for easy reference.
• A dark horizontal line is drawn to indicate the end of the hypotheses.
• A dark horizontal line is drawn along the left edge of the proof, and of each subproof.
• In addition to the basic theorems of , we have two rules that use subproofs:
• $$\Rightarrow$$-introduction