This page contain my misc math articles and essays not fitting to other categories on my math site.
Theorem (with proof), expanding and generalizing the following statement:
For two binary relations f and g the formula g = f|_{dom g} is equivalent to conjunction of g being a subset of f and the formula
g g^{-1} = f g^{-1} (or equivalently g g^{-1} = g f^{-1}).