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Generalize the definition of Subset #29

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tonyxty opened this issue Oct 14, 2020 · 0 comments
Open

Generalize the definition of Subset #29

tonyxty opened this issue Oct 14, 2020 · 0 comments

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@tonyxty
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tonyxty commented Oct 14, 2020

Subsets are currently only defined for Monoids:

-- | A subset of a monoid.
\class Subset (M : Monoid)
| \fix 8 contains : M -> \Prop
\instance SubsetPoset {M : Monoid} : Poset (Subset M)
| <= (S S' : Subset M) => \Pi (x : M) -> S.contains x -> S'.contains x
| <=-reflexive x p => p
| <=-transitive S1<=S2 S2<=S3 x p => S2<=S3 x (S1<=S2 x p)
| <=-antisymmetric S1<=S2 S2<=S1 => path (\lam i => \new Subset M (\lam x => propExt (S1<=S2 x) (S2<=S1 x) @ i))

while they can be defined for BaseSets. It goes without saying that this is useful in general.

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