Sentence examples for hence proposition from inspiring English sources
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.
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, 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.
Considering the above, then, similarly to Example 4, one can show that ρ x is weakly rejection time consistent, but it is not weakly acceptance time consistent, for any fixed (xin mathbb {R}_), and hence, by Proposition 12 and Proposition 13, α is semi-weakly rejection time consistent but not semi-weakly acceptance time consistent.
Hence, the proposition is proved.
end{aligned} Hence, the proposition is proved.
