diff options
| -rw-r--r-- | Bidir.agda | 9 |
1 files changed, 8 insertions, 1 deletions
@@ -131,4 +131,11 @@ lemma-map-denumerate-enumerate (a ∷ as) = cong (_∷_ a) (begin as ∎) theorem-1 : (get : {α : Set} → List α → List α) → {τ : Set} → (eq : EqInst τ) → (s : List τ) → bff get eq s (get s) ≡ just s -theorem-1 get eq s = {!!} +theorem-1 get eq s = begin + bff get eq s (get s) + ≡⟨ cong (bff get eq s ∘ get) (sym (lemma-map-denumerate-enumerate s)) ⟩ + bff get eq s (get (map (denumerate s) (enumerate s))) + ≡⟨ cong (bff get eq s) (free-theorem-list-list get (denumerate s) (enumerate s)) ⟩ + bff get eq s (map (denumerate s) (get (enumerate s))) + ≡⟨ {!!} ⟩ + just s ∎ |