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lines changed Original file line number Diff line number Diff line change @@ -32,6 +32,7 @@ import Relation.Binary.Definitions as Binary using (_Respectsˡ_; Irrelevant)
3232import Relation.Binary.PropositionalEquality.Core as ≡
3333 using (_≡_; cong; sym; subst)
3434open import Relation.Nary using (∀[_]; _⇒_)
35+ open import Relation.Nullary.Negation.Core using (contradiction)
3536
3637open Setoid S renaming (Carrier to A)
3738
@@ -132,7 +133,7 @@ module _ {R : Rel A r} (R⇒≉ : ∀[ R ⇒ _≉_ ]) where
132133 open ≤-Reasoning
133134
134135 step : ∀ {y} → y ∈ xs → y ∈ (ys ─ x∈ys)
135- step {y} y∈xs = fromInj₂ (λ x≈y → ⊥-elim (x∉xs (≈-subst-∈ (sym x≈y) y∈xs)))
136+ step {y} y∈xs = fromInj₂ (λ x≈y → contradiction ( (≈-subst-∈ (sym x≈y) y∈xs)) x∉xs )
136137 $ remove-inv x∈ys (inj y∈xs)
137138
138139
@@ -147,6 +148,6 @@ module _ {R : Rel A r} (R⇒≉ : ∀[ R ⇒ _≉_ ]) (≈-irrelevant : Binary.I
147148 ∈-irrelevant (there x∈xs₁) (there x∈xs₂) = ≡.cong there (∈-irrelevant x∈xs₁ x∈xs₂)
148149 -- absurd cases
149150 ∈-irrelevant {xs = cons x xs pr} (here x≈y) (there x∈xs₂) =
150- ⊥-elim (distinct x∈xs₂ (fresh⇒∉ R⇒≉ pr) x≈y )
151+ contradiction x≈y (distinct x∈xs₂ (fresh⇒∉ R⇒≉ pr))
151152 ∈-irrelevant {xs = cons x xs pr} (there x∈xs₁) (here x≈y) =
152- ⊥-elim (distinct x∈xs₁ (fresh⇒∉ R⇒≉ pr) x≈y )
153+ contradiction x≈y (distinct x∈xs₁ (fresh⇒∉ R⇒≉ pr))
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