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GAP 4.8.9 installation with standard packages -- copy to your CoCalc project to get it

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\begin{sequent}

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\begin{align*}

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  A:\Obj ~|~ \IsFree( A ) \vdash \IsProjective( A )

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\end{align*}

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\end{sequent}

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\begin{sequent}

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\begin{align*}

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  A:\Obj ~|~ \IsZero( A ) \vdash \IsFree( A )

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\end{align*}

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\end{sequent}

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