To echo Tiiba but more formally: given a specific physical circumstance (transistors designed to do a computation) you can predict the result of the computation exactly and arbitrarily quickly (or as fast as you can look it up), because you have already done that computation.

For more abstract theorems, proving two things are equivalent leads me to expect one in the presence of the other.

For example, before proving Fermat's Last Theorem, I might expect there to be a right triangle whose three sides were squares of integers. Now I expect not to.