In a previous post, I discussed what I called “Proof by definition”. However, some authors reserve that term for the solution of problems such as “Prove that every even number is divisible by two.”
Given that I was talking about something a little less trivial, it might have been better to call the kind of proof I was discussing Proof by definition substitution or some other description indicating that the solution becomes clear once you have substituted in the definitions.
On the page http://www.abstractmath.org/MM/MMFormsProof.htm Charles Wells describes this as “proof by rewriting according to the definition of the words in the theorem”. So perhaps proof by rewriting would be a short alternative. This term is, however, already used in Functional Programming, or at least I have found it used on the page
so it might be necessary to check that there is no clash of ideas there.
Meanwhile, I have added some new questions to my “routine” question sheet
More practice with definitions, proofs and examples