define a more useful version of lemma-just\==nnothing

If one had a parameter of type just x \== nothing it could be simply
refuted by case splitting. So the cases where lemma-just\==nnothing was
used always employed trans to combine two results. The new version takes
both results instead.

3 files changed, 6 insertions, 6 deletions

diff --git a/Bidir.agda b/Bidir.agda
index 3dbdbdd..d8bbf8c 100644
--- a/Bidir.agda
+++ b/Bidir.agda
@@ -53,7 +53,7 @@ lemma-lookupM-assoc i is x xs h    p | just h' = apply-checkInsertProof i x h' r
       lookupM i (insert i x h')
         ≡⟨ lemma-lookupM-insert i x h' ⟩
       just x ∎
-  ; wrong = λ x' x≢x' lookupM≡justx' → lemma-just≢nothing (trans (sym p) (lemma-checkInsert-wrong i x h' x' x≢x' lookupM≡justx'))
+  ; wrong = λ x' x≢x' lookupM≡justx' → lemma-just≢nothing p (lemma-checkInsert-wrong i x h' x' x≢x' lookupM≡justx')
   }
 
 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 → (i ∉ toList is) → lookupM i h ≡ nothing
@@ -83,7 +83,7 @@ lemma-assoc-domain (i' ∷ is') (x' ∷ xs') h ph | just h' | [ ph' ] = apply-ch
       (Data.List.All.map
         (λ {i} p → proj₁ p , lemma-lookupM-checkInsert i i' (proj₁ p) x' h' h (proj₂ p) ph)
         (lemma-assoc-domain is' xs' h' ph'))
-  ; wrong = λ x'' x'≢x'' lookupM-i'-h'≡just-x'' → lemma-just≢nothing (trans (sym ph) (lemma-checkInsert-wrong i' x' h' x'' x'≢x'' lookupM-i'-h'≡just-x''))
+  ; wrong = λ x'' x'≢x'' lookupM-i'-h'≡just-x'' → lemma-just≢nothing ph (lemma-checkInsert-wrong i' x' h' x'' x'≢x'' lookupM-i'-h'≡just-x'')
   }
 
 lemma-map-lookupM-insert : {m n : ℕ} → (i : Fin n) → (is : Vec (Fin n) m) → (x : Carrier) → (h : FinMapMaybe n Carrier) → i ∉ (toList is) → map (flip lookupM (insert i x h)) is ≡ map (flip lookupM h) is
diff --git a/CheckInsert.agda b/CheckInsert.agda
index 4083720..dd752be 100644
--- a/CheckInsert.agda
+++ b/CheckInsert.agda
@@ -74,7 +74,7 @@ lemma-checkInsert-restrict f i is = apply-checkInsertProof i (f i) (restrict f i
 lemma-lookupM-checkInsert : {n : ℕ} → (i j : Fin n) → (x y : Carrier) → (h h' : FinMapMaybe n Carrier) → lookupM i h ≡ just x → checkInsert j y h ≡ just h' → lookupM i h' ≡ just x
 lemma-lookupM-checkInsert i j x y h h' pl ph' with lookupM j h | inspect (lookupM j) h
 lemma-lookupM-checkInsert i j x y h .(insert j y h) pl refl | nothing | pl' with i ≟ j
-lemma-lookupM-checkInsert i .i x y h .(insert i y h) pl refl | nothing | [ pl' ] | yes refl = lemma-just≢nothing (trans (sym pl) pl')
+lemma-lookupM-checkInsert i .i x y h .(insert i y h) pl refl | nothing | [ pl' ] | yes refl = lemma-just≢nothing pl pl'
 lemma-lookupM-checkInsert i j x y h .(insert j y h) pl refl | nothing | pl' | no ¬p = begin
   lookupM i (insert j y h)
     ≡⟨ sym (lemma-lookupM-insert-other i j y h ¬p) ⟩
diff --git a/FinMap.agda b/FinMap.agda
index 2b50920..8b4103b 100644
--- a/FinMap.agda
+++ b/FinMap.agda
@@ -46,8 +46,8 @@ union m1 m2 = fromFunc (λ f → maybe′ id (lookup f m2) (lookupM f m1))
 restrict : {A : Set} {n : ℕ} → (Fin n → A) → List (Fin n) → FinMapMaybe n A
 restrict f is = fromAscList (zip is (map f is))
 
-lemma-just≢nothing : {A Whatever : Set} {a : A} → _≡_ {_} {Maybe A} (just a) nothing → Whatever
-lemma-just≢nothing ()
+lemma-just≢nothing : {A Whatever : Set} {a : A} {ma : Maybe A} → ma ≡ just a → ma ≡ nothing  → Whatever
+lemma-just≢nothing refl ()
 
 lemma-insert-same : {τ : Set} {n : ℕ} → (m : FinMapMaybe n τ) → (f : Fin n) → (a : τ) → lookupM f m ≡ just a → m ≡ insert f a m
 lemma-insert-same []               ()      a p
@@ -72,7 +72,7 @@ just-injective : {A : Set} → {x y : A} → _≡_ {_} {Maybe A} (just x) (just
 just-injective refl = refl
 
 lemma-lookupM-restrict : {A : Set} {n : ℕ} → (i : Fin n) → (f : Fin n → A) → (is : List (Fin n)) → (a : A) → lookupM i (restrict f is) ≡ just a → f i ≡ a
-lemma-lookupM-restrict i f [] a p = lemma-just≢nothing (trans (sym p) (lemma-lookupM-empty i))
+lemma-lookupM-restrict i f [] a p = lemma-just≢nothing p (lemma-lookupM-empty i)
 lemma-lookupM-restrict i f (i' ∷ is) a p with i ≟ i'
 lemma-lookupM-restrict i f (.i ∷ is) a p | yes refl = just-injective (begin
    just (f i)