The phrase "a proof of a" is correct and usable in written English.
It can be used in contexts where you are referring to evidence or verification of something, typically in academic or formal writing.
Example: "The researcher presented a proof of a theorem that had puzzled mathematicians for decades."
Alternatives: "evidence of a" or "verification of a".
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.
Their tutor showed them a proof of a theorem published in the 1800s, repeated in textbooks ever since, and they found a logical flaw in the theorem that no one had noticed before.
From the Greeks came a proof of a general rule for finding all such sets of numbers (now called Pythagorean triples): if one takes any whole numbers p and q, both being even or both odd, then a = (p2 − q2)/2, b = pq, and c = (p2 + q2)/2.
According to the BHK-interpretation this statement holds intuitionistically if the creating subject knows a proof of $A$ or a proof that $A$ cannot be proved.
Decidability means that at present for any given $n$ there exists (can be constructed) a proof of $A(n)$ or of $\neg A(n)$.
In particular, a proof of \(A \rightarrow B\) was no longer a construction that could be applied to any proof of \(A\) Two examples in \(\mathsf{J}\) are presented, showing modal theorems of \(\mathsf{K}\), and realizations for them.
In a lecture in 1923, Brouwer presented a proof of ¬¬¬A ⇔ ��A (Brouwer 1925E, 253)/(Mancosu 1998, 291).[8] This equivalence is the one theorem in propositional logic that Brouwer ever published.
The negation $\neg A$ of a formula $A$ is proven once it has been shown that there cannot exist a proof of $A$, which means providing a construction that derives falsum from any possible proof of $A$.
