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37 lines
853 B
Idris
37 lines
853 B
Idris
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module Data.Bool.Extra
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public export
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andSameNeutral : (x : Bool) -> x && x = x
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andSameNeutral False = Refl
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andSameNeutral True = Refl
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public export
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andFalseFalse : (x : Bool) -> x && False = False
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andFalseFalse False = Refl
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andFalseFalse True = Refl
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public export
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andTrueNeutral : (x : Bool) -> x && True = x
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andTrueNeutral False = Refl
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andTrueNeutral True = Refl
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public export
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orSameNeutral : (x : Bool) -> x || x = x
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orSameNeutral False = Refl
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orSameNeutral True = Refl
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public export
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orFalseNeutral : (x : Bool) -> x || False = x
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orFalseNeutral False = Refl
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orFalseNeutral True = Refl
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public export
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orTrueTrue : (x : Bool) -> x || True = True
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orTrueTrue False = Refl
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orTrueTrue True = Refl
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public export
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orSameAndRightNeutral : (x, right : Bool) -> x || (x && right) = x
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orSameAndRightNeutral False _ = Refl
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orSameAndRightNeutral True _ = Refl
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