Sentence examples for hence propositions from inspiring English sources
Hence, Propositions 9.1 9.2 and the multiscale nature of the problem induced by the trace-class noise suggests a procedure how to approximate the rate function and the associated LDP in practice.
This answer is given in a slightly different way at (§7) where Wittgenstein asks "may there not be true propositions which are written in this [Russell's] symbolism, but are not provable in Russell's system?", and then answers "'True propositions', hence propositions which are true in another system, i.e. can rightly be asserted in another game".
Hence Proposition 5.The proposition, in exchange for allowing slot machines in perpetuity for any tribe that wants them, requires a portion of gaming money to be spread among non-gaming tribes (a practice already in place) and other sums to go to education, health and welfare.
Hence, Proposition 8.1 proves (ii).
Hence Proposition 3.1 is satisfied.
Hence, Proposition 5.3 implies that (lambda =2).
end{aligned} Hence, Proposition 3.2 follows.
Hence, Proposition 1.5 can be considered as a substitute of (1.7).
Since 1 ≤ p, we have 1 ≤ q, and hence Proposition 2.2 immediately follows from Theorem 2.1.
Hence, Proposition 1.1 ensures that condition (1.5) holds with ρ = ρ 1.
