Sentence examples for previous proposition from inspiring English sources

Note that Proposition A.3 is also a straightforward consequence of Claim (vi) in the previous proposition.

The following example illustrates the previous proposition.

This is a contradiction to the previous proposition.  .

The following corollary is a consequence of the previous proposition.

This is a contradiction to the previous proposition.

Using the previous proposition, we have the following theorem.

Only about 20% of the budget is open to negotiation; the rest is either hypothecated by previous propositions, mandated by federal law or tied up with guaranteed pensions and salaries for state employees, including teachers.

In conclusion the hypotheses of the previous propositions are satisfied.

This demonstration cites no previous propositions or axioms of the Ethics; indeed Spinoza claims his principle of inertia is "self-evident".

According to Bolzano, a mathematical theory should be presented in the form of an axiomatic theory, whose propositions are deduced from previous propositions according to their objective dependence and eventually from the axioms.

Based on the results from previous propositions, we can derive a sharp threshold of global existence and blowup for the solution ((u x, t),n x, t), V x, t))) to the periodic initial value problem (1 - 5) in terms of the relationship between the initial energy (E u_{0}, u_{1},n_{0}, V_{0})) and (d_{Phi}>0).