Theorem
Some theorems are trivial, since they directly follow from the propositions. Other theorems are called "deep", because their proof is long and difficult. Sometimes, such proofs involve other areas of mathematics or show connections between different areas. A theorem might be simple to state and yet be deep. An excellent example is Fermat's Last Theorem, and there are many other examples of simple yet deep theorems in number theory and combinatorics (among other areas).