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simplify isSet<SomeAlgebraicStructure> #1033

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MatthiasHu
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This PR simplifies, or at least harmonizes, the definitions of the following lemmas:

isSetGroup
isSetRing
isSetDistLattice
isSetCommAlgebra
isSetLeftModule
isSetField
isSetAlgebra
isSetLattice
isSetCommRing
isSetAbGroup
isSetOrderedCommMonoid
isSetCommMonoid

Each of them is a simple is-set after opening the respective <Something>Str. In the case of Algebra and OrderedCommMonoid, the is-set field was impossible to use since it was exported twice from the respective records; I fixed that by hiding one copy (as it was already done in Ring, for example).

@@ -139,7 +139,7 @@ module _ ((G , abgroupstr _ _ _ GisGroup) : AbGroup ℓ) where
AbGroup→CommMonoid .snd .CommMonoidStr.isCommMonoid .IsCommMonoid.·Comm = IsAbGroup.+Comm GisGroup

isSetAbGroup : (A : AbGroup ℓ) → isSet ⟨ A ⟩
isSetAbGroup A = isSetGroup (AbGroup→Group A)
isSetAbGroup A = is-set (str A)
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This is the single case where the open ...Str ... method was impractical, since the file already opens multiple records with is-set fields.

@felixwellen
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Thanks for the nice refactoring!

@felixwellen felixwellen merged commit 21ddf92 into agda:master Aug 25, 2023
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2 participants