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 for antisymmetric
From The Free On-line Dictionary of Computing (30 December 2018) :

      A relation R is antisymmetric if,
      for all x and y,  x R y and y R x  =>  x == y.
     I.e. no two different elements are mutually related.
     Partial orders and total orders are antisymmetric.  If R
     is also symmetric, i.e.
      x R y  =>  y R x
      x R y  =>  x == y
     I.e. different elements are not related.

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