The phrase "a particular proof" is correct and usable in written English.
It can be used when referring to a specific example or instance of proof in a discussion or argument, particularly in academic or logical contexts.
Example: "In mathematics, we often rely on a particular proof to demonstrate the validity of a theorem."
Alternatives: "a specific proof" or "an individual proof".
For me it's much more about an argument, a line of thinking, or a particular proof," she says.
He mentioned a dispute that he had had years earlier with a collaborator over how to credit the author of a particular proof, and said that he was dismayed by the discipline's lax ethics.
Intuitively, if soundness and completeness have been established for a particular proof system and a given model-centered account of consequence, then the two accounts agree with each other: there is a proof of an argument if and only if there is no counterexample to it.
For example, whether a given connective is uniquely characterized in the sense of being governed by rules which when reduplicated to govern a new connective render compounds formed from the same component sentences using the original and the new connective completely interchangeable is relative not just to a logic but to a particular proof system (set of rules systematizing the logic).
Belnap's discussion suggests that the existence of a connective obeying certain rules should be conceded by someone endorsing a particular proof system if and only if the addition of that connective to the language and those rules to the proof system yields a conservative extension.
This means that for any particular proof in ZF, there is a set M which might as well be the universe (because any proof uses only finitely many axioms).
The list of suspect institutes is particularly sensitive, explains a State Department official, because it includes "some entities about which there is a suspicion but no particular proof" that their scientists are aiding Iran.
"If you had built a more utilitarian structure, there's no particular proof that you'd get that sort of throughput," he says.
We should be very wary of staking everything on proving or disproving a particular scientific proof.
A "general proposition" is senseless prior to an inductive proof "because the question would only have made sense if a general method of decision had been known before the particular proof was discovered" (PG 402).
But while New York, New Jersey and the District of Columbia were also among the top sources of itemized donations to Ms. Warren — and while her California donations came from all over the state — it is Hollywood that the Brown campaign has seized on as particular proof that Ms. Warren does not deserve election in Massachusetts.
