I have another proof I'm trying to complete in Coq involving the Divmod function, but the inductive case has a different value of q for the divmod function.
The q parameter is only involved in the divisor, so it shouldn't affect the remainder part of the function.
I can't find a way to prove that snd (divmod x y q u) = snd (divmod x y (S q) u) however.
The q parameter is only involved in the divisor, but because q only goes up, not down in the inductive definition, I haven't been able to prove this statement about divmod.