Results from inoculation experiment I satisfied Hill's criterion 4 [22] of "time sequence" (cause precedes effect) by demonstrating successful infectivity following putative pathogen inoculations.
Five subjects of Group I satisfied the CRS-R criteria for a minimally conscious state during the observation period (Supplementary Table 1).
Thus, the Bayesian abstract fuzzy economy G = { ( Ω, F, μ ), ( X i, F i, A i, P i, a i, b i, z i ) i ∈ I } satisfies all hypotheses of Theorem 1.
To sum up, I satisfies ( I 3 ) of Lemma 2.2.
Next, we show that I satisfies ( I 3 ) of Lemma 2.2.
Proof We will show that I satisfies the hypotheses of Lemma 2.2.
We now show that there exist constants (rho>0) and (alpha>0) such that I satisfies condition (A1) of Lemma 2.6.
Moreover, I satisfies the reduct of our program with respect to J.
A non-ground rule r (resp., a program π) is satisfied by an interpretation I iff I satisfies all groundings of r (resp., Gr. I ⊆ B U is an answer set of π iff it is a subset-minimal set satisfying the Gelfond Lifschitz reduct π I = { H (r ) ← B + (r ) | I ∩ B − (r ) = ∅, r ∈ Gr }.
We will verify that I satisfies all the conditions of Theorem B.
Now we show that I satisfies the geometry conditions of mountain pass theorem.
