I'm just starting playing with idris and theorem proving in general. I can follow most of the examples of proofs of basic facts on the internet, so I wanted to try something arbitrary by my own. So, I want to write a proof term for the following basic property of map:
map : (a -> b) -> List a -> List b
prf : map id = id
Intuitively, I can imagine how the proof should work: Take an arbitrary list l and analyze the possibilities for map id l. When l is empty, it's obvious; when l is non-empty it's based on the concept that function application preserves equality. So, I can do something like this:
prf' : (l : List a) -> map id l = id l
It's like a for all statement. How can I turn it into a proof of the equality of the functions involved?