30 lines
864 B
Text
30 lines
864 B
Text
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/-
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Copyright (c) 2015 Microsoft Corporation. All rights reserved.
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Released under Apache 2.0 license as described in the file LICENSE.
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Author: Leonardo de Moura
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(set A) is an instance of a commutative semiring
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-/
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import data.set.basic algebra.ring
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open algebra set
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definition set_comm_semiring [instance] (A : Type) : comm_semiring (set A) :=
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⦃ comm_semiring,
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add := union,
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mul := inter,
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zero := empty,
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one := univ,
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add_assoc := union.assoc,
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add_comm := union.comm,
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zero_add := empty_union,
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add_zero := union_empty,
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mul_assoc := inter.assoc,
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mul_comm := inter.comm,
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zero_mul := empty_inter,
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mul_zero := inter_empty,
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one_mul := univ_inter,
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mul_one := inter_univ,
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left_distrib := inter.distrib_left,
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right_distrib := inter.distrib_right
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⦄
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