51 lines
1 KiB
Text
51 lines
1 KiB
Text
inductive list (A : Type) : Type :=
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nil {} : list A,
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cons : A → list A → list A
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section
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parameter A : Type
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inductive list2 : Type :=
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nil2 {} : list2,
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cons2 : A → list2 → list2
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end
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variable num : Type.{1}
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namespace Tree
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inductive tree (A : Type) : Type :=
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node : A → forest A → tree A
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with forest (A : Type) : Type :=
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nil : forest A,
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cons : tree A → forest A → forest A
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end Tree
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inductive group_struct (A : Type) : Type :=
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mk_group_struct : (A → A → A) → A → group_struct A
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inductive group : Type :=
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mk_group : Π (A : Type), (A → A → A) → A → group
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section
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parameter A : Type
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parameter B : Type
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inductive pair : Type :=
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mk_pair : A → B → pair
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end
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definition Prop := Type.{0}
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inductive eq {A : Type} (a : A) : A → Prop :=
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refl : eq a a
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section
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parameter {A : Type}
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inductive eq2 (a : A) : A → Prop :=
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refl2 : eq2 a a
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end
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section
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parameter A : Type
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parameter B : Type
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inductive triple (C : Type) : Type :=
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mk_triple : A → B → C → triple C
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end
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