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But the 45-year-old South African, who has won two Open and two US Open titles, is living proof of no guarantees when it comes to winning at Augusta.
The same reasoning as in the proof of Theorem 3.3, guarantees there exists a unique C-linear mapping (delta :Arightarrow A) satisfying (32).
While in this case the policeman involved has been fired and charged, such a degree of proof is no guarantee of justice.
Even APIs with a formal proof of security may not guarantee absolute security when used in a real-world device or application.
One alternative is known as "proof of stake". Rather than asking people to solve resource-intensive computational puzzles, a proof-of-stake system requires issuers to put up capital as a guarantee.
Also, the nonexpansiveness of f is used in the proof of Theorem 6.1 only to guarantee the existence of an approximate fixed point sequence for f and to guarantee that f is continuous.
(For students and those over 60, though there's no guarantee foreign proof of age or student status will be accepted).
In Section 2, we apply a simple consequence of Keller's chain rule, devoted to the proof of the sufficient conditions which guarantee that every solution of (1.2) oscillates or converges to zero.
Notice that the only application of the nonempty closed bounded condition in Theorem 3.1 in the proof of Theorem 3.1 is to guarantee that the subset is a subcomplete -sublattice of.
Documents prepared by the notary or authenticated in the proper manner are, in these countries, admissible in court without further proof of their authenticity; the notary guarantees the identity of the parties.
The tax increase, the ministry added, "constitutes a proof of the government's determination to guarantee the deficit targets for this year".
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Since I tried Ludwig back in 2017, I have been constantly using it in both editing and translation. Ever since, I suggest it to my translators at ProSciEditing.

Justyna Jupowicz-Kozak
CEO of Professional Science Editing for Scientists @ prosciediting.com