Sentence examples for proof of assumption from inspiring English sources

This concludes the proof of assumption 1.

So like in the proof of assumption (i) of Theorem 3.1, we can get (4.11).

It is similar to the proof of assumption (i) of Theorem 3.1; we can easily get that (4.8).

The latter is actually a visual proof of assumptions voiced many years ago about a mutual effect of gas and dust on observed polarization of comets (see, for instance, a historical review in Kiselev et al., 2015).

In the proof of Theorem 1.1, the condition that for, in (F1), is only used in the the proofs of assumption (ii) of Lemma 2.1.

Several authors supposed the generation of p-benzoquinone (PBQ; Table 2) from PPD under oxidation conditions relevant for the formation of azo (hair) dyes, but a reliable proof of the assumption is missing [3, 16, 49, 50].

Further elucidation of these processes is required to make firm conclusions regarding this controversial issue, and consistent proof of this assumption may be extremely relevant in clinics because of the disputed role of platelets in sepsis and questions regarding therapeutic intervention in life-threatening sepsis patients.

Soon leads to a guilt trip because no matter what, your refutation is proof of the assumption.

While we do not have a rigorous proof of these assumptions, they have been confirmed by extensive simulations.

Proof In view of assumption (d), the contractivity condition d ( f x, f y ) ≤ φ ( d ( g x, g y ) ) holds for any x, y ∈ X under two possibilities: either g ( x ) ⪯ g ( y ) or g ( x ) ⪰ g ( y ).

In one sense, this is just practical proof of a working assumption.