32 lines
980 B
Text
32 lines
980 B
Text
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/-
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Copyright (c) 2015 Leonardo de Moura. All rights reserved.
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Released under Apache 2.0 license as described in the file LICENSE.
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Authors: Leonardo de Moura
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Finite type (type class)
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-/
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import data.list data.bool
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open list bool unit decidable
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structure fintype [class] (A : Type) : Type :=
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(elems : list A) (unique : nodup elems) (complete : ∀ a, a ∈ elems)
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definition fintype_unit [instance] : fintype unit :=
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fintype.mk [star] dec_trivial (λ u, match u with star := dec_trivial end)
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definition fintype_bool [instance] : fintype bool :=
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fintype.mk [ff, tt]
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dec_trivial
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(λ b, match b with | tt := dec_trivial | ff := dec_trivial end)
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definition fintype_product [instance] {A B : Type} : fintype A → fintype B → fintype (A × B)
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| (fintype.mk e₁ u₁ c₁) (fintype.mk e₂ u₂ c₂) :=
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fintype.mk
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(cross_product e₁ e₂)
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(nodup_cross_product u₁ u₂)
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(λ p,
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match p with
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(a, b) := mem_cross_product (c₁ a) (c₂ b)
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end)
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