then the following implication is valid: if (p=p^{r}_{0}(x)), then mathbb{P} left widetilde{V}_{T} (x,p,phi,mathcal{C})=x right)=1.
Moreover, if condition (i) holds, then condition (ii) is equivalent to the following condition if p is such that there exists ((x,p,phi,mathcal {C} in Psi ^{0,x} (p,mathcal {C})) satisfying mathbb{P} left widetilde{V}_{T} (x,p,phi,mathcal{C}) geq x right)=1, (53) then the following implication is valid: if (p=p^{r}_{0}(x)), then mathbb{P} left widetilde{V}_{T} (x,p,phi,mathcal{C})=x right)=1.
It is clear that the following diagram, where arrows stand for implications, is valid: contraction → quasicontraction ↓ ↓ ordered contraction → ordered quasicontraction.
Furthermore, the reverse implications are valid.
From the above definition, it is easy to see that the following implications are valid: E is uniformly convex ⇒ E is locally uniformly convex ⇒ E is strictly convex.
In other words, the implications are valid regarding the knowledge formalised in the Boolean network and can also be checked by supplementary human expert knowledge or further literature research, e.g., for co-regulation of genes or possible or forbidden resulting states.
Indeed, the above theorem assures us that the implication '⇐' is valid.
Lemma 4.14 Assume that the estimator is quasi-monotone (3.8) and that the implication (4.25) is valid for one particular choice of 0 < κ 0, θ 0<1 1.
Therefore, the implication NADH.out.0 → ROS.out.2 is valid.
We can do it by restricting ourselves to models in which we have the validity of If we require \eqref{eq16}, quantification over objects is reducible to intensional quantification: More precisely, the implication \(\eqref{eq16} \supset \eqref{eq17}\) is valid in FOIL semantics.
44 45 To the extent the explanation is valid, an implication of our study is that clinicians need to be aware of, and sensitive to, aspects of 'maleness,' including men's help-seeking behaviours and communication patterns, so as to present information in a way men feel comfortable with.
