In type checking, particularly in dependent types, it is not trivial to check that two types are the same. Different notions of equality are useful in this fiel

In type checking, particularly in dependent types, it is not trivial to check that two types are the same. Different notions of equality are useful in this field. A type can contain a function value inside. How to prove that two functions are the same? Is not enough to prove that for all X f X and g X implies f is g.