Proof construction is the process of creating a logical argument that demonstrates the truth of a mathematical statement. It involves using established definitions, theorems, and logical reasoning to build a sequence of statements that lead to a conclusion. This method ensures that the argument is valid and can be followed step-by-step. In mathematics, proof construction often employs various techniques, such as direct proof, indirect proof, or proof by contradiction. Each technique has its own approach to establishing the validity of a statement, allowing mathematicians to explore different ways to confirm their findings and contribute to the broader field of mathematical logic.