Direct proof

A direct proof is a way of showing that something is true or false by using logic. This is done by combining known facts. No assumptions are made when doing a direct proof. Lemmas and theorems are used to prove direct proofs.
A statement that can be proved with a direct proof is usually in the form "if "p", then "q"." Here, "p" and "q" are facts. To solve a statement like this, every case where "p" is true must be considered.
For example, this statement can be solved with a direct proof: "if x and y are even integers, then x+y is an even integer." Since x and y are even, then we can say that "x=2m" and "y=2n," where "m" and "n" are integers. (This is a lemma.) We can also say that "m+n" is an integer, because adding two integers gives an integer. (This is another lemma.) Then we can say that "x+y=2m+2n=2(m+n)". Since "m+n" is an integer, we can say "2(m+n)=2k", where "k=m+n". We know that any integer times 2 is an even integer. We can then say that any two even integers added together give an even integer.
Direct proofs are used in mathematics, logic, and computer science. The opposite of a direct proof is an indirect proof (also called a "proof by contradiction".)