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[ refactor ] remove last uses of inspect in Data.Rational.Unnormalised.Properties #2926

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Merged
jamesmckinna merged 1 commit into from
Jan 30, 2026
Merged

[ refactor ] remove last uses of inspect in Data.Rational.Unnormalised.Properties #2926

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24 changes: 12 additions & 12 deletions src/Data/Rational/Unnormalised/Properties.agda
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Original file line number Diff line number Diff line change
Expand Up @@ -1542,24 +1542,24 @@ p>1⇒1/p<1 {p} p>1 = lemma′ p (p>1⇒p≢0 p>1) p>1
-- Basic specification in terms of _≤_

p≤q⇒p⊔q≃q : p ≤ q → p ⊔ q ≃ q
p≤q⇒p⊔q≃q {p@record{}} {q@record{}} p≤q with p ≤ᵇ q | inspect (p ≤ᵇ_) q
... | true | _ = ≃-refl
... | false | [ p≰q ] = contradiction (≤⇒≤ᵇ p≤q) (subst (¬_ ∘ T) (sym p≰q) λ())
p≤q⇒p⊔q≃q {p@record{}} {q@record{}} p≤q with p ≤ᵇ q in eq
... | true = ≃-refl
... | false = contradiction (≤⇒≤ᵇ p≤q) (subst (¬_ ∘ T) (sym eq) λ())

p≥q⇒p⊔q≃p : p ≥ q → p ⊔ q ≃ p
p≥q⇒p⊔q≃p {p@record{}} {q@record{}} p≥q with p ≤ᵇ q | inspect (p ≤ᵇ_) q
... | true | [ p≤q ] = ≤-antisym p≥q (≤ᵇ⇒≤ (subst T (sym p≤q) _))
... | false | [ p≤q ] = ≃-refl
p≥q⇒p⊔q≃p {p@record{}} {q@record{}} p≥q with p ≤ᵇ q in eq
... | true = ≤-antisym p≥q (≤ᵇ⇒≤ (subst T (sym eq) _))
... | false = ≃-refl

p≤q⇒p⊓q≃p : p ≤ q → p ⊓ q ≃ p
p≤q⇒p⊓q≃p {p@record{}} {q@record{}} p≤q with p ≤ᵇ q | inspect (p ≤ᵇ_) q
... | true | _ = ≃-refl
... | false | [ p≰q ] = contradiction (≤⇒≤ᵇ p≤q) (subst (¬_ ∘ T) (sym p≰q) λ())
p≤q⇒p⊓q≃p {p@record{}} {q@record{}} p≤q with p ≤ᵇ q in eq
... | true = ≃-refl
... | false = contradiction (≤⇒≤ᵇ p≤q) (subst (¬_ ∘ T) (sym eq) λ())

p≥q⇒p⊓q≃q : p ≥ q → p ⊓ q ≃ q
p≥q⇒p⊓q≃q {p@record{}} {q@record{}} p≥q with p ≤ᵇ q | inspect (p ≤ᵇ_) q
... | true | [ p≤q ] = ≤-antisym (≤ᵇ⇒≤ (subst T (sym p≤q) _)) p≥q
... | false | [ p≤q ] = ≃-refl
p≥q⇒p⊓q≃q {p@record{}} {q@record{}} p≥q with p ≤ᵇ q in eq
... | true = ≤-antisym (≤ᵇ⇒≤ (subst T (sym eq) _)) p≥q
... | false = ≃-refl

⊓-operator : MinOperator ≤-totalPreorder
⊓-operator = record
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