The phrase "a proof of an" is correct and usable in written English.
It can be used when referring to evidence or verification of a particular claim or statement, often in academic or formal contexts.
Example: "The researcher presented a proof of an important theorem that had puzzled mathematicians for decades."
Alternatives: "evidence of a" or "verification of an".
On our way down, a young woman approached Dangin, her arm outstretched to support a proof of an ad for a men's cologne.
Setting aside any anti-skeptical intent therefore, what needs assessment is the metaphysical significance of Moore's proof, as a proof of an 'external world'.
For example, if we assume that something is a proof of an implication A → B, we need not necessarily show that both A and B are well-formed propositions outright, but, in addition to knowing that A is a proposition, we only need to know that B is a proposition provided that A has been proved.
The history of mathematics has shown that making a "detour" through higher mathematics can sometimes lead to a proof of an arithmetical statement that is much shorter and that provides more insight than any purely arithmetical proof of the same statement.
A proof of an implication A ⊃ B, say, is a program that converts data of type A into an output of type B. The construction of an object (proof, function, program) f of the type A ⊃ B ends with an abstraction.
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.
PA never insists (proves) that a proof of A entails A's truth, unless it already has a proof of A to back up that claim.
In 1887 Markov's teacher Pafnuty Chebyshev outlined a proof of a generalized central limit theorem.
Unlike proof in law or science, which is based on evidence and therefore subject to qualification and revision, a proof of a theorem is definitive.
When I produce a proof of A Jar of Wild Flowers, he turns it over in his hands in delighted surprise.
This excludes neither finding a proof of A nor finding a proof of ¬A later.
