The phrase "need not establish" is correct and usable in written English.
You can use this phrase to indicate that something does not have to be done or is unnecessary. For example, "You need not establish a new account if you already have one."
Different from the unbalanced random key predistribution scheme [18] as described in Section 2, in which L2 nodes must establish secure connections with the L1 nodes, in RPKE, the auxiliary nodes need not establish the pairwise key with the ordinary nodes or other auxiliary nodes.
The Enterprise need not establish a new organization, but could evolve from existing international organizations.
Note that in order to undercut an argument for τ one need not establish that τ doesn't hold.
Anonymous You needn't establish precedence between your two ideals; instead you should find a way to oppose an abhorrent practice while avoiding cultural imperialism.
These power relations need not be expressly established and defined in law.
In United States v. Cook (1872), the Court held that indictments need not plead facts establishing that these limitations periods have not run.
Field geologists always prize a layer that is so distinctive in appearance that a series of tests need not be made to establish its identity.
Further quantitative proteomic studies are needed not only to establish the expression levels of these proteins in each PD variant, but also to establish the protein levels associated with health.
Long-term study are needed, not only to establish the effectiveness of different airways clearance devices or techniques and their cost-effectiveness, but especially to establish their acceptability in order to long-term home use.
The inquiry is needed not only to establish the truth but to restore public trust.
The minister said answers were needed not only to establish accountability but because they were "critical to improving child protection practice across the country".
