individually open ≡-Reasoning

_≡⟨_⟩_ will be turned into a syntax, so it cannot be imported in future.
Avoid doing so now by opening it where needed.

2 files changed, 35 insertions, 29 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 : ℕ} → (i : Fin n) → (f : Fin n �
 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
diff --git a/Precond.agda b/Precond.agda
index 9d21022..623c99f 100644
--- a/Precond.agda
+++ b/Precond.agda
@@ -23,8 +23,7 @@ open import Data.Maybe using (just)
 open import Data.Product using (∃ ; _,_ ; proj₁ ; proj₂)
 open import Function using (flip ; _∘_ ; id)
 open import Relation.Binary using (Setoid)
-open import Relation.Binary.PropositionalEquality as P using (inspect ; [_])
-open P.≡-Reasoning using (begin_ ; _≡⟨_⟩_ ; _∎)
+open import Relation.Binary.PropositionalEquality as P using (inspect ; [_] ; module ≡-Reasoning)
 open import Relation.Nullary using (yes ; no)
 
 open import Structures using (IsFunctor ; module Shaped ; Shaped)
@@ -49,13 +48,15 @@ lemma-union-delete-fromFunc {is = []} h {g = g} p = _ , (tabulate-cong (λ f →
       maybe′ just (just (g f)) (lookupM f h)
         ≡⟨ lemma-maybe-just (g f) (lookupM f h) ⟩
       just (maybe′ id (g f) (lookupM f h)) ∎))
+  where open ≡-Reasoning
 lemma-union-delete-fromFunc {n = n} {is = i ∷ is} h {g = g} (Data.List.All._∷_ (x , px) ps) = _ , (begin
   union h (delete i (delete-many is (fromFunc g)))
     ≡⟨ tabulate-cong inner ⟩
   union h (delete-many is (fromFunc g))
     ≡⟨ proj₂ (lemma-union-delete-fromFunc h ps) ⟩
   _ ∎)
-  where inner : (f : Fin n) → maybe′ just (lookupM f (delete i (delete-many is (fromFunc g)))) (lookup h f) ≡ maybe′ just (lookupM f (delete-many is (fromFunc g))) (lookup h f)
+  where open ≡-Reasoning
+        inner : (f : Fin n) → maybe′ just (lookupM f (delete i (delete-many is (fromFunc g)))) (lookup h f) ≡ maybe′ just (lookupM f (delete-many is (fromFunc g))) (lookup h f)
         inner f with f ≟ i
         inner .i | yes P.refl = begin
           maybe′ just (lookupM i (delete i (delete-many is (fromFunc g)))) (lookup h i)
@@ -92,7 +93,8 @@ module _ (G : Get) where
         fmapS (Maybe.just ∘ proj₁ wp) t
           ≡⟨ IsFunctor.composition (Shaped.isFunctor SourceShapeT (gl₁ i)) just (proj₁ wp) t ⟩
         fmapS Maybe.just (fmapS (proj₁ wp) t) ∎) ⟩ _ ∎)
-    where s′ = enumerate SourceShapeT (gl₁ i)
+    where open ≡-Reasoning
+          s′ = enumerate SourceShapeT (gl₁ i)
           g  = fromFunc (denumerate SourceShapeT s)
           g′ = delete-many (contentV (get s′)) g
           t  = enumerate SourceShapeT (gl₁ i)
@@ -107,20 +109,22 @@ lemma-∉-lookupM-assoc i []         []         P.refl i∉is = lookup-replicate
 lemma-∉-lookupM-assoc i (i' ∷ is') (x' ∷ xs')     ph i∉is with assoc is' xs' | inspect (assoc is') xs'
 lemma-∉-lookupM-assoc i (i' ∷ is') (x' ∷ xs')     () i∉is | nothing | [ ph' ]
 lemma-∉-lookupM-assoc i (i' ∷ is') (x' ∷ xs') {h} ph i∉is | just h' | [ ph' ] = begin
-  lookupM i h
-    ≡⟨ lemma-lookupM-checkInsert-other i i' (i∉is ∘ here) x' h' ph ⟩
-  lookupM i h'
-    ≡⟨ lemma-∉-lookupM-assoc i is' xs' ph' (i∉is ∘ there) ⟩
-  nothing ∎
+    lookupM i h
+      ≡⟨ lemma-lookupM-checkInsert-other i i' (i∉is ∘ here) x' h' ph ⟩
+    lookupM i h'
+      ≡⟨ lemma-∉-lookupM-assoc i is' xs' ph' (i∉is ∘ there) ⟩
+    nothing ∎
+  where open ≡-Reasoning
 
 different-assoc : {m n : ℕ} → (u : Vec (Fin n) m) → (v : Vec Carrier m) → All-different (toList u) → ∃ λ h → assoc u v ≡ just h
 different-assoc []       []       p = empty , P.refl
 different-assoc (u ∷ us) (v ∷ vs) (different-∷ u∉us diff-us) with different-assoc us vs diff-us
 different-assoc (u ∷ us) (v ∷ vs) (different-∷ u∉us diff-us) | h , p' = insert u v h , (begin
-  assoc (u ∷ us) (v ∷ vs)
-    ≡⟨ P.refl ⟩
-  (assoc us vs >>= checkInsert u v)
-    ≡⟨ P.cong (flip _>>=_ (checkInsert u v)) p' ⟩
-  checkInsert u v h
-    ≡⟨ lemma-checkInsert-new u v h (lemma-∉-lookupM-assoc u us vs p' u∉us) ⟩
-  just (insert u v h) ∎)
+    assoc (u ∷ us) (v ∷ vs)
+      ≡⟨ P.refl ⟩
+    (assoc us vs >>= checkInsert u v)
+      ≡⟨ P.cong (flip _>>=_ (checkInsert u v)) p' ⟩
+    checkInsert u v h
+      ≡⟨ lemma-checkInsert-new u v h (lemma-∉-lookupM-assoc u us vs p' u∉us) ⟩
+    just (insert u v h) ∎)
+  where open ≡-Reasoning