Idris - proof of inductive step

Question

Consider the following function

tryMove : (diskNumber : Nat) -> (from: Peg) -> (to: Peg)-> {default Oh prf: So (from /= to)} -> Disposition diskNumber -> Maybe (Disposition diskNumber)
tryMove Z from to [] = Nothing
tryMove (S k) from to (smallestDiskPosition :: restOfTheDisposition) =
        map (smallestDiskPosition ::) (tryMove k from to restOfTheDisposition)

Trying to compile, I get the following error:

When checking argument prf to Hanoi.tryMove:
        Type mismatch between
                So True (Type of Oh)
        and
                So (from /= to) (Expected type)

        Specifically:
                Type mismatch between
                        True
                and
                        not (Hanoi.Peg implementation of Prelude.Interfaces.Eq, method == from to)

when calling recurvise tryMove. If I explicitly convey {prf}, as in

tryMove : (diskNumber : Nat) -> (from: Peg) -> (to: Peg)-> {default Oh prf: So (from /= to)} -> Disposition diskNumber -> Maybe (Disposition diskNumber)
tryMove Z from to [] = Nothing
tryMove (S k) from to {prf} (smallestDiskPosition :: restOfTheDisposition) =
        map (smallestDiskPosition ::) (tryMove k from to {prf} restOfTheDisposition)

It compiles correctly.

Why can't Idris automatically detect evidence at the inductive step, while he is able to do this with a normal function call?

EDIT:

here is the full meaning: https://gist.github.com/marcosh/d51479ea08e8522560713fd1e5ca9624

Answer 1

(Oh) prf, Oh . Oh So True, , prf So (from /= to), to from, from /= to, . .

, {auto prf: So (from /= to)}, prf, , - .