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Correct statement for weakening preservation.
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This is to unify parts of Environment and Substition.
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This is in anticipation of a proof that composition preserves IsNotId.
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Almost no users of the view use this proof. Hide the details from users.
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This is in anticipation for defining well-formed thinnings.
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There correspond to lemmata 2.1--2.5 in Abel et. al.
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