Sentence examples for a proven conclusion from inspiring English sources

The summary paragraphs concluding many chapters of his book ascribe the woes and upheavals they cover to the results of "the climatic chaos of the mid-sixth century," and readers may see this constantly repeated assertion more as a ritual credo than a proven conclusion.

Now we prove conclusion (I).

Next, we prove conclusion (2).

We prove conclusion (i) first.

Next, we prove conclusion (II).

Here, we prove conclusion (b).

To prove conclusion (i), we suppose that (langle x_{1}rangle^>0).

Note that Lemma 3.7 proves conclusion (2) of Theorem 3.5.

Then Eq. (4.1) has a unique positive solution x ∗ ( t ) satisfying 10 − 2 ≤ x ∗ ( t ) ≤ 1. Proof We use Theorem 3.3 to prove Conclusion 4.1.

Next, we prove conclusions (i) and (ii) hold for (M_{Omega,alpha}).

Noting that statements (i) and (ii) hold followed by (iii)–(v), we will only prove conclusions (iii)–(v).