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Add symmetric and transitive closure relations
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@ -127,3 +127,59 @@ PartialEquivalence ty Equal where
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public export
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public export
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Equivalence ty Equal where
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Equivalence ty Equal where
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----------------------------------------
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public export
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data SymClosure : Rel ty -> ty -> ty -> Type where
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Fwd : {0 x, y : ty} -> rel x y -> SymClosure rel x y
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Bwd : {0 x, y : ty} -> rel y x -> SymClosure rel x y
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public export
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Reflexive ty rel => Reflexive ty (SymClosure rel) where
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reflexive = Fwd reflexive
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public export
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Symmetric ty (SymClosure rel) where
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symmetric (Fwd xy) = Bwd xy
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symmetric (Bwd yx) = Fwd yx
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----------------------------------------
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public export
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data TransClosure : Rel ty -> ty -> ty -> Type where
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Nil : TransClosure rel x x
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(::) : {y : ty} -> rel x y -> TransClosure rel y z -> TransClosure rel x z
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public export
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Reflexive ty (TransClosure rel) where
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reflexive = []
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public export
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Symmetric ty rel => Symmetric ty (TransClosure rel) where
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symmetric {x} {y} xy = reverseOnto [] xy
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where
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reverseOnto : {z : ty} ->
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TransClosure rel z x ->
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TransClosure rel z y ->
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TransClosure rel y x
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reverseOnto zx [] = zx
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reverseOnto zx (zw :: wy) = reverseOnto (symmetric zw :: zx) wy
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public export
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Transitive ty (TransClosure rel) where
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transitive [] yz = yz
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transitive (xw :: wy) yz = xw :: transitive wy yz
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public export
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Symmetric ty rel => Euclidean ty (TransClosure rel) where
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euclidean = euclidean @{TSE}
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public export
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Symmetric ty rel => Tolerance ty (TransClosure rel) where
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public export
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Symmetric ty rel => PartialEquivalence ty (TransClosure rel) where
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public export
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Symmetric ty rel => Equivalence ty (TransClosure rel) where
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@ -906,12 +906,12 @@ groupAllWith f = groupWith f . sortBy (comparing f)
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-- Nil is not Cons
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-- Nil is not Cons
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export
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export
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Uninhabited ([] = x :: xs) where
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{0 xs : List a} -> Uninhabited ([] = x :: xs) where
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uninhabited Refl impossible
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uninhabited Refl impossible
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-- Cons is not Nil
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-- Cons is not Nil
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export
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export
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Uninhabited (x :: xs = []) where
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{0 xs : List a} -> Uninhabited (x :: xs = []) where
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uninhabited Refl impossible
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uninhabited Refl impossible
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-- If the heads or the tails of two lists are provably non-equal, then the
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-- If the heads or the tails of two lists are provably non-equal, then the
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@ -109,21 +109,25 @@ LOG elab.ambiguous:5: Ambiguous elaboration at Vec:L:C--L:C:
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($resolvedN 2)
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($resolvedN 2)
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($resolvedN 2)
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($resolvedN 2)
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With default. Target type : Prelude.Types.Nat
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With default. Target type : Prelude.Types.Nat
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LOG elab.ambiguous:5: Ambiguous elaboration (kept 3 out of 3 candidates) (not delayed) at Vec:L:C--L:C:
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LOG elab.ambiguous:5: Ambiguous elaboration (kept 4 out of 4 candidates) (not delayed) at Vec:L:C--L:C:
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(($resolvedN Nil) ((:: ((:: (fromInteger 0)) Nil)) Nil))
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(($resolvedN Nil) ((:: ((:: (fromInteger 0)) Nil)) Nil))
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(($resolvedN Nil) ((:: ((:: (fromInteger 0)) Nil)) Nil))
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(($resolvedN Nil) ((:: ((:: (fromInteger 0)) Nil)) Nil))
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(($resolvedN Nil) ((:: ((:: (fromInteger 0)) Nil)) Nil))
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(($resolvedN Nil) ((:: ((:: (fromInteger 0)) Nil)) Nil))
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(($resolvedN Nil) ((:: ((:: (fromInteger 0)) Nil)) Nil))
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Target type : ({arg:N} : (Data.Fin.Fin (Prelude.Types.S (Prelude.Types.S Prelude.Types.Z)))) -> (Prelude.Basics.List Prelude.Types.Nat)
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Target type : ({arg:N} : (Data.Fin.Fin (Prelude.Types.S (Prelude.Types.S Prelude.Types.Z)))) -> (Prelude.Basics.List Prelude.Types.Nat)
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LOG elab.ambiguous:5: Ambiguous elaboration (kept 2 out of 2 candidates) (not delayed) at Vec:L:C--L:C:
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LOG elab.ambiguous:5: Ambiguous elaboration (kept 3 out of 3 candidates) (not delayed) at Vec:L:C--L:C:
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$resolvedN
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$resolvedN
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$resolvedN
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$resolvedN
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$resolvedN
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Target type : ?Vec.{a:N}_[]
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Target type : ?Vec.{a:N}_[]
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LOG elab.ambiguous:5: Ambiguous elaboration (kept 3 out of 3 candidates) (not delayed) at Vec:L:C--L:C:
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LOG elab.ambiguous:5: Ambiguous elaboration (kept 4 out of 4 candidates) (not delayed) at Vec:L:C--L:C:
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(($resolvedN ((:: (fromInteger 0)) Nil)) Nil)
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(($resolvedN ((:: (fromInteger 0)) Nil)) Nil)
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(($resolvedN ((:: (fromInteger 0)) Nil)) Nil)
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(($resolvedN ((:: (fromInteger 0)) Nil)) Nil)
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(($resolvedN ((:: (fromInteger 0)) Nil)) Nil)
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(($resolvedN ((:: (fromInteger 0)) Nil)) Nil)
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(($resolvedN ((:: (fromInteger 0)) Nil)) Nil)
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Target type : (Vec.Vec ?Vec.{a:N}_[] ?Vec.{n:N}_[])
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Target type : (Vec.Vec ?Vec.{a:N}_[] ?Vec.{n:N}_[])
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LOG elab.ambiguous:5: Ambiguous elaboration (kept 3 out of 3 candidates) (not delayed) at Vec:L:C--L:C:
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LOG elab.ambiguous:5: Ambiguous elaboration (kept 4 out of 4 candidates) (not delayed) at Vec:L:C--L:C:
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(($resolvedN (fromInteger 0)) Nil)
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(($resolvedN (fromInteger 0)) Nil)
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(($resolvedN (fromInteger 0)) Nil)
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(($resolvedN (fromInteger 0)) Nil)
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(($resolvedN (fromInteger 0)) Nil)
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(($resolvedN (fromInteger 0)) Nil)
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(($resolvedN (fromInteger 0)) Nil)
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@ -132,26 +136,32 @@ LOG elab.ambiguous:5: Ambiguous elaboration at Vec:L:C--L:C:
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($resolvedN 0)
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($resolvedN 0)
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($resolvedN 0)
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($resolvedN 0)
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With default. Target type : ?Vec.{a:N}_[]
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With default. Target type : ?Vec.{a:N}_[]
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LOG elab.ambiguous:5: Ambiguous elaboration (kept 2 out of 2 candidates) (not delayed) at Vec:L:C--L:C:
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LOG elab.ambiguous:5: Ambiguous elaboration (kept 3 out of 3 candidates) (not delayed) at Vec:L:C--L:C:
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$resolvedN
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$resolvedN
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$resolvedN
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$resolvedN
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$resolvedN
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Target type : (Vec.Vec ?Vec.{a:N}_[] ?Vec.{n:N}_[])
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Target type : (Vec.Vec ?Vec.{a:N}_[] ?Vec.{n:N}_[])
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LOG elab.ambiguous:5: Ambiguous elaboration at Vec:L:C--L:C:
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($resolvedN 0)
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($resolvedN 0)
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With default. Target type : (?Vec.{rel:N}_[] ?Vec.{x:N}_[] ?Vec.{y:N}_[])
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LOG elab.ambiguous:5: Ambiguous elaboration at Vec:L:C--L:C:
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LOG elab.ambiguous:5: Ambiguous elaboration at Vec:L:C--L:C:
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($resolvedN 0)
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($resolvedN 0)
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($resolvedN 0)
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($resolvedN 0)
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With default. Target type : ?Vec.{a:N}_[]
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With default. Target type : ?Vec.{a:N}_[]
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LOG elab.ambiguous:5: Ambiguous elaboration (kept 2 out of 2 candidates) (not delayed) at Vec:L:C--L:C:
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LOG elab.ambiguous:5: Ambiguous elaboration (kept 3 out of 3 candidates) (not delayed) at Vec:L:C--L:C:
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$resolvedN
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$resolvedN
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$resolvedN
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$resolvedN
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$resolvedN
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Target type : (Vec.Vec ?Vec.{a:N}_[] ?Vec.{n:N}_[])
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Target type : (Vec.Vec ?Vec.{a:N}_[] ?Vec.{n:N}_[])
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LOG elab.ambiguous:5: Ambiguous elaboration (kept 1 out of 3 candidates) (delayed) at Vec:L:C--L:C:
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LOG elab.ambiguous:5: Ambiguous elaboration (kept 1 out of 4 candidates) (delayed) at Vec:L:C--L:C:
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(($resolvedN (fromInteger 0)) Nil)
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(($resolvedN (fromInteger 0)) Nil)
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Target type : (Prelude.Basics.List Prelude.Types.Nat)
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Target type : (Prelude.Basics.List Prelude.Types.Nat)
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LOG elab.ambiguous:5: Ambiguous elaboration at Vec:L:C--L:C:
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LOG elab.ambiguous:5: Ambiguous elaboration at Vec:L:C--L:C:
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($resolvedN 0)
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($resolvedN 0)
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($resolvedN 0)
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($resolvedN 0)
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With default. Target type : Prelude.Types.Nat
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With default. Target type : Prelude.Types.Nat
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LOG elab.ambiguous:5: Ambiguous elaboration (kept 1 out of 2 candidates) (delayed) at Vec:L:C--L:C:
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LOG elab.ambiguous:5: Ambiguous elaboration (kept 1 out of 3 candidates) (delayed) at Vec:L:C--L:C:
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$resolvedN
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$resolvedN
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Target type : (Prelude.Basics.List Prelude.Types.Nat)
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Target type : (Prelude.Basics.List Prelude.Types.Nat)
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LOG declare.def:2: Case tree for Vec.test: [0] (Vec.:: (Prelude.Types.S Prelude.Types.Z) (Prelude.Basics.List Prelude.Types.Nat) (Prelude.Basics.Nil Prelude.Types.Nat) (Vec.:: Prelude.Types.Z (Prelude.Basics.List Prelude.Types.Nat) (Prelude.Basics.:: Prelude.Types.Nat Prelude.Types.Z (Prelude.Basics.Nil Prelude.Types.Nat)) (Vec.Nil (Prelude.Basics.List Prelude.Types.Nat))))
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LOG declare.def:2: Case tree for Vec.test: [0] (Vec.:: (Prelude.Types.S Prelude.Types.Z) (Prelude.Basics.List Prelude.Types.Nat) (Prelude.Basics.Nil Prelude.Types.Nat) (Vec.:: Prelude.Types.Z (Prelude.Basics.List Prelude.Types.Nat) (Prelude.Basics.:: Prelude.Types.Nat Prelude.Types.Z (Prelude.Basics.Nil Prelude.Types.Nat)) (Vec.Nil (Prelude.Basics.List Prelude.Types.Nat))))
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@ -14,6 +14,7 @@ Main> Error: Can't find an implementation for Num ().
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^^^^
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^^^^
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Main> Error: Ambiguous elaboration. Possible results:
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Main> Error: Ambiguous elaboration. Possible results:
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Control.Relation.Nil
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Prelude.Nil
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Prelude.Nil
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Data.Vect.Nil
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Data.Vect.Nil
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