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Relation/Binary/Construct/NaturalOrder
3 files changed +12
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lines changed Original file line number Diff line number Diff line change @@ -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
Original file line number Diff line number Diff line change @@ -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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------------------------------------------------------------------------
Original file line number Diff line number Diff line change @@ -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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