Sentence examples for are not superfluous from inspiring English sources
In a sense, that's not exactly true because the thoughts and feelings are not superfluous.
These internal mechanisms are not superfluous to the President's adherence to the law but are a reflection of the executive branch's legal commitments spanning administrations.
Example 5.7 shows that the assumptions in Theorem 5.9 are not superfluous.
In response to this sort of objection, Wallace (2011) argues that the reactive emotions are not superfluous add-ons to the judgment, but instead they serve to change the meaning of the judgment, imbuing the judgment with the sort of expressive significance that is characteristic of blame and that would otherwise be lacking from a mere judgment.
Consider the set (mathcal{P}^{0}_{mathrm{swapping}}) of two-qubit couplings that contains at least one qubit in the unit cell 0. Define (mathfrak{W}) as the set of TLR schemes that include all TLRs that are not superfluous with respect to (mathcal{P}_{mathrm{swapping}}^{0}) and all their equivalent TLRs.
The preventive 6 h3 is not superfluous.
Because Saʿadia believed that humans have a priori knowledge of good and evil and that this knowledge coincides with the principles underlying the most important portions of the revealed law, he was forced to ask whether this law is not superfluous.
The assumption about the soft compactness in Theorem 6.1 is not superfluous.
In this theorem, the assumption on the dimension of the complex and of the manifold is not superfluous; in fact, Xiaosong presents in [6, Section 4] a map from the bitorus into the torus with and.
"Only where the state ends, there begins the human being who is not superfluous" (Z I:11) Of course, it is only the latter individual that really interests Nietzsche.
