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$x$ is a real antisymmetric matrix and is defined as:

Format[x[a_, b_]] := Subscript[x, a, b]
    $Assumptions = 
      x \[Element] Matrices[{4, 4}, Reals, Antisymmetric[{1, 2}]];
    x[arg__] /; ! OrderedQ@{arg} := Signature@{arg} x @@ Sort@{arg} 
    Format[x[arg__]] := Subscript[x, arg]

x[2,2] is expected to get zero. That is any repeated indices is zero. How to implement it in the above code?

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  • $\begingroup$ x[a_, b_] := 1/2 (Array[A, {5, 5}] - Transpose@Array[A, {5, 5}])[[a, b]]; x[2,2] ? $\endgroup$
    – cvgmt
    Jul 17 at 12:14
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I think the following works

Format[x[a_, b_]] := Subscript[x, a, b]
$Assumptions = 
  x ∈ Matrices[{4, 4}, Reals, Antisymmetric[{1, 2}]];
x[arg__] /; SameQ[arg] := 0
x[arg__] /; ! OrderedQ@{arg} := Signature@{arg} x @@ Sort@{arg}

Your !OrderedQ test is not triggered for the diagonal elements.

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