Find centralized, trusted content and collaborate around the technologies you use most.
Teams
Q&A for work
Connect and share knowledge within a single location that is structured and easy to search.
The problem is that the first equation can also be used for s+ ◃ y. Only after you know that y is not zero, the second equation applies.
s+ ◃ y
y
The solution is simple:
lemma : ∀ y → s+ ◃ y ≡ + y lemma zero = refl lemma (suc _) = refl