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merge: Quotient and fmset ++-assoc (#1103)
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12 changes: 12 additions & 0 deletions
12
cli-impl/src/test/resources/shared/src/algebra/free-group.aya
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Original file line number | Diff line number | Diff line change |
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open import prelude | ||
|
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open inductive FreeGroup (A : Type) | ||
| η A | ||
| infixl · (a b : FreeGroup A) tighter = | ||
| ε | ||
| inv (FreeGroup A) | ||
| assoc (x y z : FreeGroup A) : x · (y · z) = (x · y) · z | ||
| idr (x : FreeGroup A) : x = x · ε | ||
| idl (x : FreeGroup A) : x = ε · x | ||
| invr (x : FreeGroup A) : x · (inv x) = ε | ||
| invl (x : FreeGroup A) : (inv x) · x = ε |
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12 changes: 12 additions & 0 deletions
12
cli-impl/src/test/resources/shared/src/relation/binary/quotient.aya
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Original file line number | Diff line number | Diff line change |
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open import prelude hiding (map) | ||
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open inductive infix / (A : Type) (R : Fn (a b : A) → Type) tighter = | ||
| in~ A | ||
| eq~ {a b : A} (R a b) : in~ a = in~ b | ||
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variable A B : Type | ||
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def map {R : ∀ a b → Type} {Q : ∀ a b → Type} (f : A → B) | ||
(p : ∀ a a' → R a a' → Q (f a) (f a')) (q : A / R) : B / Q elim q | ||
| in~ a => in~ (f a) | ||
| eq~ r i => eq~ (p _ _ r) i |
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