The phrase "argument establishes" is correct and usable in written English.
It can be used when discussing the role of an argument in supporting a claim or position in a debate or academic context.
Example: "The argument establishes a clear connection between the evidence presented and the conclusion drawn."
Alternatives: "argument supports" or "argument demonstrates".
One part of the argument establishes a bound and the other shows that such bound is attainable.
An intuitive solution-doubling argument establishes well known results concerning the worst-case performance of spanning tree-based heuristics for the Steiner network problem and the traveling salesman problem.
A parallel argument establishes subalternation from E to O as well.
It's not entirely clear that this argument establishes that people are not compound things.
If sound, Broad's argument establishes the negative conclusion that mental phenomena are distinct from neurophysiological processes.
He argues that strictly speaking, Aristotle's argument establishes only that the world is perpetual, not that it is eternal.
In this note we present a combinatorial argument establishing that no 3-SAT instance on n variables can have a prime implicate whose length exceeds max {[n/2] + 1, [2n/3]}, validating this conjecture for the case n = 9.
Procrastinators should like this argument: Establishing a foundation or charitable trust means an immediate income tax writeoff, but the decision about which cause to benefit can be postponed.
"Even if there were no other argument establishing that [the denial of free will] is false, this alone ought to be sufficiently persuasive" (p. 338).
If we accept Clifton's statistical reasoning, we have an entirely valid KS argument establishing a contradiction between an HV interpretation of QM and the very predictions of QM.
Next, we specify a class of functions with certain regularity properties and using a compactness argument establish the convergence of smooth solutions to the solution of the original problem with piecewise constant initial density (rho_{0}).
