How to prove $g(d,\ f(g(d,\ d),\ d,\ d))$ as a correct term in Predicate Logic

Question

I have been learning Predicate Logic recently and I get a following question:

Assumed $\ F = \{m,\ f\}, P = \{S,\ B\}$, in which $m$ is constant, $f$ is ternary function, $g$ is binary function, prove $g(d,\ f(g(d,\ d),\ d,\ d))$ as a correct Term in Predicate Logic.

I want to prove it by drawing a parse tree or inductive reasoning, but I don't know the which one is mathematical rigor.

If not mind, could anyone tell me the mathematical rigor way to prove the correctness of Term and Formula in Predicate Logic and prove it?

Thanks in advance.

Answer 1

An inductive proof is used to prove a statement about a general class of objects, but in this case you only have one specific object, so an inductive argument is not the appropriate tool to use here.

Instead, you should indeed just show that you can make a valid parse tree for this expression.