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[ add ] obvious lemma about self-contradiction to Relation.Nullary.Negation.Core #2693

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Merged
merged 3 commits into from
Apr 23, 2025
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[ add ] obvious lemma about self-contradiction to Relation.Nullary.Negation.Core #2693

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fc2ca8a
add: obvious lemma about self-contradiction
jamesmckinna Apr 10, 2025
e9403ed
add: obvious lemma about self-contradiction
jamesmckinna Apr 10, 2025
0ec848b
fix: change name
jamesmckinna Apr 17, 2025
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5 changes: 5 additions & 0 deletions CHANGELOG.md
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Expand Up @@ -244,3 +244,8 @@ Additions to existing modules
⊤-dec : Dec {a} ⊤
⊥-dec : Dec {a} ⊥
```

* In `Relation.Nullary.Negation.Core`:
```agda
contra-diagonal : (A → ¬ A) → ¬ A
```
5 changes: 5 additions & 0 deletions src/Relation/Nullary/Negation/Core.agda
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Expand Up @@ -60,6 +60,11 @@ contradiction₂ (inj₂ b) ¬a ¬b = contradiction b ¬b
contraposition : (A → B) → ¬ B → ¬ A
contraposition f ¬b a = contradiction (f a) ¬b

-- Self-contradictory propositions are false by 'diagonalisation'

contra-diagonal : (A → ¬ A) → ¬ A
contra-diagonal self a = self a a

-- Everything is stable in the double-negation monad.
stable : ¬ ¬ Stable A
stable ¬[¬¬a→a] = ¬[¬¬a→a] (contradiction (¬[¬¬a→a] ∘ const))
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