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Fixes #2166 by fixing names in IsSemilattice (#2211)
* Fix names in IsSemilattice * Add reference to changes to Semilattice to CHANGELOG
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CHANGELOG.md

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@@ -205,7 +205,9 @@ Non-backwards compatible changes
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* Added new `IsBoundedSemilattice`/`BoundedSemilattice` records.
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* Added new aliases `Is(Meet/Join)(Bounded)Semilattice` for `Is(Bounded)Semilattice`
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which can be used to indicate meet/join-ness of the original structures.
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which can be used to indicate meet/join-ness of the original structures, and
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the field names in `IsSemilattice` and `Semilattice` have been renamed from
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`∧-cong` to `∙-cong`to indicate their undirected nature.
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* Finally, the following auxiliary files have been moved:
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```agda

src/Algebra/Lattice/Structures.agda

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@@ -37,30 +37,25 @@ record IsSemilattice (∙ : Op₂ A) : Set (a ⊔ ℓ) where
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comm : Commutative ∙
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open IsBand isBand public
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renaming
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( ∙-cong to ∧-cong
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; ∙-congˡ to ∧-congˡ
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; ∙-congʳ to ∧-congʳ
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)
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-- Used to bring names appropriate for a meet semilattice into scope.
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IsMeetSemilattice = IsSemilattice
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module IsMeetSemilattice {∧} (L : IsMeetSemilattice ∧) where
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open IsSemilattice L public
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renaming
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( -cong to ∧-cong
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; -congˡ to ∧-congˡ
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; -congʳ to ∧-congʳ
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( -cong to ∧-cong
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; -congˡ to ∧-congˡ
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; -congʳ to ∧-congʳ
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)
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-- Used to bring names appropriate for a join semilattice into scope.
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IsJoinSemilattice = IsSemilattice
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module IsJoinSemilattice {∨} (L : IsJoinSemilattice ∨) where
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open IsSemilattice L public
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renaming
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( -cong to ∨-cong
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; -congˡ to ∨-congˡ
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; -congʳ to ∨-congʳ
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( -cong to ∨-cong
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; -congˡ to ∨-congˡ
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; -congʳ to ∨-congʳ
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)
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------------------------------------------------------------------------

src/Relation/Binary/Construct/NaturalOrder/Left.agda

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@@ -99,21 +99,21 @@ module _ (semi : IsSemilattice _∙_) where
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x∙y≤x : x y (x ∙ y) ≤ x
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x∙y≤x x y = begin
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x ∙ y ≈⟨ -cong (sym (idem x)) S.refl ⟩
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x ∙ y ≈⟨ -cong (sym (idem x)) S.refl ⟩
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(x ∙ x) ∙ y ≈⟨ assoc x x y ⟩
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x ∙ (x ∙ y) ≈⟨ comm x (x ∙ y) ⟩
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(x ∙ y) ∙ x ∎
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x∙y≤y : x y (x ∙ y) ≤ y
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x∙y≤y x y = begin
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x ∙ y ≈⟨ -cong S.refl (sym (idem y)) ⟩
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x ∙ y ≈⟨ -cong S.refl (sym (idem y)) ⟩
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x ∙ (y ∙ y) ≈⟨ sym (assoc x y y) ⟩
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(x ∙ y) ∙ y ∎
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∙-presʳ-≤ : {x y} z z ≤ x z ≤ y z ≤ (x ∙ y)
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∙-presʳ-≤ {x} {y} z z≤x z≤y = begin
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z ≈⟨ z≤y ⟩
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z ∙ y ≈⟨ -cong z≤x S.refl ⟩
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z ∙ y ≈⟨ -cong z≤x S.refl ⟩
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(z ∙ x) ∙ y ≈⟨ assoc z x y ⟩
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z ∙ (x ∙ y) ∎
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