Sentence examples for proven formally from inspiring English sources

Such results are proven formally in Theorems 3.2 and 3.3.

Let us go back to a classical HD case, where the (consistent) conjunction \(h \wedge k\) (but not \ k\) alone) entails \ e.\) The following can be proven: Formally, it is fairly simple to show that (SP) characterizes relevance confirmation (see, e.g., Crupi, Festa, and Buttasi 2010, 80; Hájek and Joyce 2008, 123), but the philosophical import of this result is nonetheless remarkable.

In [ 21] (Theorem 1, part 1) it was proven formally that the number of irrRAFs within an RAF can grow exponentially with the size of the RAF.

Conservation of energy, momentum and angular momentum is proved formally and numerically.

Our theoretical framework allows us to prove formally that our algorithms are correct.

The aim is to prove formally, before implementation, their correctness w.r.t. the required properties such as achieving safely the expected services (soundness property).

However, it is to be emphasized that the above question indeed seems neither simple nor evident, and its proposition cannot be proved formally.

The following theorem, which is attributed to Condorcet and was first proved formally by Laplace, shows that if there are only two options, then majority rule is, in fact, the best procedure from an epistemic point of view.

He proved formally that there is no Turing machine which can determine, in a finite number of steps, whether or not any given formula of the predicate calculus is a theorem of the calculus.

Note that ∂Ω is sufficiently smooth, the energy estimates can be proved formally multiplying (1) by (u^{delta}) for (i), (u^{delta}_{t}) for (ii), and (tu^{delta}_{t}) for (iii).

In this paper, we use the design approach for fitting the proportional hazards (PH) model and prove formally the asymptotic normality of the sample maximum partial likelihood (SMPL) estimators under the PH model for both stochastically independent and clustered failure times.