Function extensionality
= Function extensionality
{title2=$f=g\iff\forall x\in A,\ f(x)=g(x)$}
For two mathematical <functions> $f,g:A\to B$ with the same domain and codomain, equality is equivalent to equality of their values at every argument. In the set-theoretic representation, their <graphs of functions> then contain exactly the same ordered pairs. This permits a function identity to be proved by fixing an arbitrary argument and proving the resulting value equality.