66 lines
1.3 KiB
Text
66 lines
1.3 KiB
Text
inductive Foo
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| mk1 | mk2 | mk3
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deriving BEq
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namespace Foo
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theorem ex1 : (mk1 == mk2) = false :=
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rfl
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theorem ex2 : (mk1 == mk1) = true :=
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rfl
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theorem ex3 : (mk2 == mk2) = true :=
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rfl
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theorem ex4 : (mk3 == mk3) = true :=
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rfl
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theorem ex5 : (mk2 == mk3) = false :=
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rfl
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end Foo
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inductive Vec (α : Type u) : Nat → Type u
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| nil : Vec α 0
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| cons : α → {n : Nat} → Vec α n → Vec α (n+1)
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deriving BEq
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namespace Vec
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theorem ex1 : (cons 10 Vec.nil == cons 20 Vec.nil) = false :=
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rfl
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theorem ex2 : (cons 10 Vec.nil == cons 10 Vec.nil) = true :=
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rfl
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theorem ex3 : (cons 20 (cons 11 Vec.nil) == cons 20 (cons 10 Vec.nil)) = false :=
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rfl
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theorem ex4 : (cons 20 (cons 11 Vec.nil) == cons 20 (cons 11 Vec.nil)) = true :=
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rfl
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end Vec
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inductive Bla (α : Type u) where
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| node : List (Bla α) → Bla α
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| leaf : α → Bla α
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deriving BEq
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namespace Bla
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#eval node [] == leaf 10
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#eval node [leaf 10] == node [leaf 10]
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#eval node [leaf 10] == node [leaf 10, leaf 20]
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end Bla
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mutual
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inductive Tree (α : Type u) where
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| node : TreeList α → Tree α
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| leaf : α → Tree α
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deriving BEq
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inductive TreeList (α : Type u) where
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| nil : TreeList α
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| cons : Tree α → TreeList α → TreeList α
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deriving BEq
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end
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def ex1 [BEq α] : BEq (Tree α) :=
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inferInstance
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def ex2 [BEq α] : BEq (TreeList α) :=
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inferInstance
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