replace FinMap.lemma-lookupM-empty with Data.Vec.Properties.lookup-replicate

2 files changed, 6 insertions, 10 deletions

diff --git a/FinMap.agda b/FinMap.agda
index df422c3..1ae4c39 100644
--- a/FinMap.agda
+++ b/FinMap.agda
@@ -6,7 +6,7 @@ open import Data.Maybe using (Maybe ; just ; nothing ; maybe′)
 open import Data.Fin using (Fin ; zero ; suc)
 open import Data.Fin.Properties using (_≟_)
 open import Data.Vec using (Vec ; [] ; _∷_ ; _[_]≔_ ; replicate ; tabulate ; foldr ; zip ; toList) renaming (lookup to lookupVec ; map to mapV)
-open import Data.Vec.Properties using (lookup∘update ; lookup∘update′)
+open import Data.Vec.Properties using (lookup∘update ; lookup∘update′ ; lookup-replicate)
 open import Data.Product using (_×_ ; _,_)
 open import Data.List.All as All using (All)
 import Data.List.All.Properties as AllP
@@ -79,12 +79,8 @@ lemma-insert-same         []       ()      p
 lemma-insert-same {suc n} (x ∷ xs) zero    p = P.cong (flip _∷_ xs) p
 lemma-insert-same         (x ∷ xs) (suc i) p = P.cong (_∷_ x) (lemma-insert-same xs i p)
 
-lemma-lookupM-empty : {A : Set} {n : ℕ} → (i : Fin n) → lookupM {A} i empty ≡ nothing
-lemma-lookupM-empty zero    = P.refl
-lemma-lookupM-empty (suc i) = lemma-lookupM-empty i
-
 lemma-lookupM-restrict : {A : Set} {n m : ℕ} → (i : Fin n) → (f : Fin n → A) → (is : Vec (Fin n) m) → {a : A} → lookupM i (restrict f is) ≡ just a → f i ≡ a
-lemma-lookupM-restrict i f []            p = contradiction (P.trans (P.sym p) (lemma-lookupM-empty i)) (λ ())
+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)
@@ -108,7 +104,7 @@ lemma-lookupM-restrict-∈ i f (j ∷ js) (Any.there p)  | no i≢j =
           (lemma-lookupM-restrict-∈ i f js p)
 
 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) ≡ nothing
-lemma-lookupM-restrict-∉ i f []       i∉[]  = lemma-lookupM-empty i
+lemma-lookupM-restrict-∉ i f []       i∉[]  = lookup-replicate i nothing
 lemma-lookupM-restrict-∉ i f (j ∷ js) i∉jjs =
   P.trans (lookup∘update′ (All.head i∉jjs) (restrict f js) (just (f j)))
           (lemma-lookupM-restrict-∉ i f js (All.tail i∉jjs))
diff --git a/Precond.agda b/Precond.agda
index 98ba7a6..8eec6da 100644
--- a/Precond.agda
+++ b/Precond.agda
@@ -15,7 +15,7 @@ import Data.Maybe.Categorical
 open Category.Monad.RawMonad {Level.zero} Data.Maybe.Categorical.monad using (_>>=_)
 open Category.Functor.RawFunctor {Level.zero} Data.Maybe.Categorical.functor using (_<$>_)
 open import Data.Vec using (Vec ; [] ; _∷_ ; map ; lookup ; toList)
-open import Data.Vec.Properties using (map-cong ; map-∘ ; tabulate-∘)
+open import Data.Vec.Properties using (map-cong ; map-∘ ; tabulate-∘ ; lookup-replicate)
 import Data.List.All
 open import Data.List.Any using (here ; there)
 open import Data.List.Membership.Setoid using (_∉_)
@@ -28,7 +28,7 @@ open P.≡-Reasoning using (begin_ ; _≡⟨_⟩_ ; _∎)
 open import Relation.Nullary using (yes ; no)
 
 open import Structures using (IsFunctor ; module Shaped ; Shaped)
-open import FinMap using (FinMapMaybe ; lookupM ; union ; fromFunc ; empty ; insert ; lemma-lookupM-empty ; delete-many ; lemma-tabulate-∘ ; delete ; lemma-lookupM-delete ; lemma-lookupM-fromFunc ; reshape ; lemma-reshape-id)
+open import FinMap using (FinMapMaybe ; lookupM ; union ; fromFunc ; empty ; insert ; delete-many ; lemma-tabulate-∘ ; delete ; lemma-lookupM-delete ; lemma-lookupM-fromFunc ; reshape ; lemma-reshape-id)
 import CheckInsert
 open CheckInsert (P.decSetoid deq) using (checkInsert ; lemma-checkInsert-new ; lemma-lookupM-checkInsert-other)
 import BFF
@@ -103,7 +103,7 @@ data All-different {A : Set} : List A → Set where
   different-∷  : {x : A} {xs : List A} → _∉_ (P.setoid A) x xs → All-different xs → All-different (x ∷ xs)
 
 lemma-∉-lookupM-assoc : {m n : ℕ} → (i : Fin n) → (is : Vec (Fin n) m) → (xs : Vec Carrier m) → {h : FinMapMaybe n Carrier} → assoc is xs ≡ just h → _∉_ (P.setoid (Fin n)) i (toList is) → lookupM i h ≡ nothing
-lemma-∉-lookupM-assoc i []         []         P.refl i∉is = lemma-lookupM-empty i
+lemma-∉-lookupM-assoc i []         []         P.refl i∉is = lookup-replicate i nothing
 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