Add a property relating maybe to composition (#2414)

* Add a property relating `maybe` to composition

* Add CHANGELOG and slightly simpler definition

* Update CHANGELOG.md

Co-authored-by: jamesmckinna <[email protected]>

---------

Co-authored-by: Jacques Carette <[email protected]>
Co-authored-by: jamesmckinna <[email protected]>

Author: 3 people

CHANGELOG.md

@@ -71,6 +71,11 @@ Additions to existing modules
   ++⁺ˡ : Reflexive R → ∀ zs → (_++ zs) Preserves (Pointwise R) ⟶ (Pointwise R)
   ```
 
+* In `Data.Maybe.Properties`:
+  ```agda
+  maybe′-∘ : ∀ f g → f ∘ (maybe′ g b) ≗ maybe′ (f ∘ g) (f b)
+  ```
+
 * New lemmas in `Data.Nat.Properties`:
   ```agda
   m≤n⇒m≤n*o : ∀ o .{{_ : NonZero o}} → m ≤ n → m ≤ n * o

src/Data/Maybe/Properties.agda

@@ -97,6 +97,9 @@ maybe′-map : ∀ j (n : C) (f : A → B) ma →
              maybe′ j n (map f ma) ≡ maybe′ (j ∘′ f) n ma
 maybe′-map = maybe-map
 
+maybe′-∘ : ∀ {b} (f : B → C) (g : A → B) → f ∘ (maybe′ g b) ≗ maybe′ (f ∘ g) (f b)
+maybe′-∘ _ _ = maybe (λ _ → refl) refl
+
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 -- _<∣>_