@@ -751,12 +751,14 @@ if-eta false = refl
751751if-eta true = refl
752752
753753if-idem-then : ∀ b {x y : A} →
754- (if b then (if b then x else y) else y) ≡ (if b then x else y)
754+ (if b then (if b then x else y) else y)
755+ ≡ (if b then x else y)
755756if-idem-then false = refl
756757if-idem-then true = refl
757758
758759if-idem-else : ∀ b {x y : A} →
759- (if b then x else (if b then x else y)) ≡ (if b then x else y)
760+ (if b then x else (if b then x else y))
761+ ≡ (if b then x else y)
760762if-idem-else false = refl
761763if-idem-else true = refl
762764
@@ -790,7 +792,8 @@ if-∨ false = refl
790792if-∨ true = refl
791793
792794if-xor : ∀ b {c} {x y : A} →
793- (if b xor c then x else y) ≡ (if b then (if c then y else x) else (if c then x else y))
795+ (if b xor c then x else y)
796+ ≡ (if b then (if c then y else x) else (if c then x else y))
794797if-xor false = refl
795798if-xor true {false} = refl
796799if-xor true {true } = refl
@@ -808,19 +811,23 @@ if-xor true {true } = refl
808811-- unfortunately fails to resolve the omitted argument.)
809812
810813if-cong : ∀ {b c} {x y : A} → b ≡ c →
811- (if b then x else y) ≡ (if c then x else y)
814+ (if b then x else y)
815+ ≡ (if c then x else y)
812816if-cong refl = refl
813817
814818if-cong-then : ∀ b {x y z : A} → x ≡ z →
815- (if b then x else y) ≡ (if b then z else y)
819+ (if b then x else y)
820+ ≡ (if b then z else y)
816821if-cong-then _ refl = refl
817822
818823if-cong-else : ∀ b {x y z : A} → y ≡ z →
819- (if b then x else y) ≡ (if b then x else z)
824+ (if b then x else y)
825+ ≡ (if b then x else z)
820826if-cong-else _ refl = refl
821827
822828if-cong₂ : ∀ b {x y z w : A} → x ≡ z → y ≡ w →
823- (if b then x else y) ≡ (if b then z else w)
829+ (if b then x else y)
830+ ≡ (if b then z else w)
824831if-cong₂ _ refl refl = refl
825832
826833------------------------------------------------------------------------
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