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djspacewhale committed Feb 16, 2025
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8 changes: 6 additions & 2 deletions src/group-theory/left-quasigroups.lagda.md
Original file line number Diff line number Diff line change
Expand Up @@ -58,9 +58,13 @@ module _

is-prop-is-left-Quasigroup : is-prop is-left-Quasigroup
is-prop-is-left-Quasigroup =
is-prop-Σ is-prop-is-left-cancellative-left-div (λ _ is-prop-is-right-cancellative-left-div)
is-prop-Σ is-prop-is-left-cancellative-left-div
( λ _ is-prop-is-right-cancellative-left-div)

left-Quasigroup : (l : Level) UU (lsuc l)
left-Quasigroup l =
Σ (Set l) (λ Q Σ (type-Set Q type-Set Q type-Set Q) (λ mul Σ (type-Set Q type-Set Q type-Set Q) λ left-div is-left-Quasigroup Q mul left-div))
Σ ( Set l)
( λ Q Σ (type-Set Q type-Set Q type-Set Q)
( λ mul Σ (type-Set Q type-Set Q type-Set Q)
( λ left-div is-left-Quasigroup Q mul left-div)))
```
8 changes: 6 additions & 2 deletions src/group-theory/right-quasigroups.lagda.md
Original file line number Diff line number Diff line change
Expand Up @@ -60,9 +60,13 @@ module _

is-prop-is-right-Quasigroup : is-prop is-right-Quasigroup
is-prop-is-right-Quasigroup =
is-prop-Σ is-prop-is-left-cancellative-right-div (λ _ is-prop-is-right-cancellative-right-div)
is-prop-Σ is-prop-is-left-cancellative-right-div
( λ _ is-prop-is-right-cancellative-right-div)

right-Quasigroup : (l : Level) UU (lsuc l)
right-Quasigroup l =
Σ (Set l) (λ Q Σ (type-Set Q type-Set Q type-Set Q) (λ mul Σ (type-Set Q type-Set Q type-Set Q) λ right-div is-right-Quasigroup Q mul right-div))
Σ ( Set l)
( λ Q Σ (type-Set Q type-Set Q type-Set Q)
( λ mul Σ (type-Set Q type-Set Q type-Set Q)
( λ right-div is-right-Quasigroup Q mul right-div)))
```

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