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12 lines
472 B
Agda
12 lines
472 B
Agda
{-# OPTIONS --safe --warning=error --without-K #-}
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open import LogicalFormulae
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open import Semirings.Definition
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module Semirings.Lemmas {a : _} {A : Set a} {Zero One : A} {_+_ _*_ : A → A → A} (S : Semiring Zero One _+_ _*_) where
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open Semiring S
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doubleIsAddTwo : (a : A) → (a + a) ≡ (One + One) * a
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doubleIsAddTwo a = transitivity (equalityCommutative (+WellDefined (productOneLeft a) (productOneLeft a))) (equalityCommutative (+DistributesOver*' One One a))
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