Sentence examples for using propositions from inspiring English sources

Finally, by using Propositions 3-5, we prove Theorem 1.

Using Propositions 1 and 2, it holds regarding Eqs.

We may run the same sort of argument using propositions instead of properties.

Now, using Propositions 3.9 and 3.10, we can give the following corollary.

Notice that this is just an instance (using propositions rather than sentences) of the previously stated axiom (5).

(26) Again, by using Propositions 1.6 and 1.7, we have (p x,Tx)=0), which gives (xin Tx).

Let us note that (H1s - H2s - H3s) imply (H1 - H2 - H3); hence, by using Proposition 2.4, ((x_{n})_{ninmathbb{N}}) is asymptotically regular.

Indeed, for all, using Proposition 2.2 no.

Using Proposition 2.4 it follows that.

Hence the result follows using Proposition 3.3.

Using Proposition 9, we get this lemma.