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Boolean/Lemmas.agda

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+{-# OPTIONS --safe --warning=error --without-K #-}
+
+open import Agda.Primitive using (Level; lzero; lsuc; _⊔_)
+open import LogicalFormulae
+open import Boolean.Definition
+
+module Boolean.Lemmas where
+
+notNot : (x : Bool) → not (not x) ≡ x
+notNot BoolTrue = refl
+notNot BoolFalse = refl
+
+notXor : (x y : Bool) → not (xor x y) ≡ xor (not x) y
+notXor BoolTrue BoolTrue = refl
+notXor BoolTrue BoolFalse = refl
+notXor BoolFalse BoolTrue = refl
+notXor BoolFalse BoolFalse = refl