1 files changed, 15 insertions, 13 deletions

diff --git a/FinMap.agda b/FinMap.agda
index 051014c..1241252 100644
--- a/FinMap.agda
+++ b/FinMap.agda
@@ -19,8 +19,7 @@ open import Function.Surjection using (module Surjection)
 open import Relation.Nullary using (yes ; no)
 open import Relation.Nullary.Negation using (contradiction)
 open import Relation.Binary.Core using (Decidable)
-open import Relation.Binary.PropositionalEquality as P using (_≡_ ; _≢_ ; _≗_)
-open P.≡-Reasoning using (begin_ ; _≡⟨_⟩_ ; _∎)
+open import Relation.Binary.PropositionalEquality as P using (_≡_ ; _≢_ ; _≗_ ; module ≡-Reasoning)
 
 _∈_ : {A : Set} {n : ℕ} → A → Vec A n → Set
 _∈_ {A} x xs = Data.List.Membership.Setoid._∈_ (P.setoid A) x (toList xs)
@@ -82,17 +81,19 @@ lemma-lookupM-restrict : {A : Set} {n m : â„•} → (i : Fin n) → (f : Fin n â†
 lemma-lookupM-restrict i f []            p = contradiction (P.trans (P.sym p) (lookup-replicate i nothing)) (λ ())
 lemma-lookupM-restrict i f (i' ∷ is)     p with i ≟ i'
 lemma-lookupM-restrict i f (.i ∷ is) {a} p | yes P.refl = just-injective (begin
-   just (f i)
-     ≡⟨ P.sym (lookup∘update i (restrict f is) (just (f i))) ⟩
-   lookupM i (insert i (f i) (restrict f is))
-     ≡⟨ p ⟩
-   just a ∎)
+    just (f i)
+      ≡⟨ P.sym (lookup∘update i (restrict f is) (just (f i))) ⟩
+    lookupM i (insert i (f i) (restrict f is))
+      ≡⟨ p ⟩
+    just a ∎)
+  where open ≡-Reasoning
 lemma-lookupM-restrict i f (i' ∷ is) {a} p | no i≢i' = lemma-lookupM-restrict i f is (begin
-  lookupM i (restrict f is)
-    ≡⟨ P.sym (lookup∘update′ i≢i' (restrict f is) (just (f i'))) ⟩
-  lookupM i (insert i' (f i') (restrict f is))
-    ≡⟨ p ⟩
-  just a ∎)
+    lookupM i (restrict f is)
+      ≡⟨ P.sym (lookup∘update′ i≢i' (restrict f is) (just (f i'))) ⟩
+    lookupM i (insert i' (f i') (restrict f is))
+      ≡⟨ p ⟩
+    just a ∎)
+  where open ≡-Reasoning
 lemma-lookupM-restrict-∈ : {A : Set} {n m : ℕ} → (i : Fin n) → (f : Fin n → A) → (js : Vec (Fin n) m) → i ∈ js → lookupM i (restrict f js) ≡ just (f i)
 lemma-lookupM-restrict-∈ i f [] ()
 lemma-lookupM-restrict-∈ i f (j ∷ js)  p             with i ≟ j
@@ -120,7 +121,8 @@ lemma-reshape-id (x ∷ xs) = P.cong (_∷_ x) (lemma-reshape-id xs)
 
 lemma-disjoint-union : {n m : ℕ} {A : Set} → (f : Fin n → A) → (t : Vec (Fin n) m) → union (restrict f t) (delete-many t (fromFunc f)) ≡ fromFunc f
 lemma-disjoint-union {n} f t = tabulate-cong inner
-  where inner : (x : Fin n) → maybe′ just (lookupM x (delete-many t (fromFunc f))) (lookupM x (restrict f t)) ≡ just (f x)
+  where open ≡-Reasoning
+        inner : (x : Fin n) → maybe′ just (lookupM x (delete-many t (fromFunc f))) (lookupM x (restrict f t)) ≡ just (f x)
         inner x with is-∈ _≟_ x t
         inner x | yes-∈ x∈t = P.cong (maybe′ just (lookupM x (delete-many t (fromFunc f)))) (lemma-lookupM-restrict-∈ x f t x∈t)
         inner x | no-∉ x∉t = begin