Specialize

To transform a theorem P into some theorem P’ that applies to a similar but more specific set of inputs than P. For example, the commutativity of addition states that

forall (n m : nat), n + m = m + n.

This can be specialized into the following theorem, which says that addition is commutative if one of the arguments is 7:

forall (m : nat), 7 + m = m + 7.

Important property: if the original general theorem P is true, then a specialized form P’ of that theorem is always true!

Synonyms: weaken Antonyms: generalize, strengthen