The phrase "a precise proof" is correct and usable in written English.
It can be used when referring to a proof that is exact, clear, and without ambiguity, often in mathematical or logical contexts.
Example: "In order to validate the theorem, we need to provide a precise proof that leaves no room for doubt."
Alternatives: "an exact proof" or "a clear proof".
A physical system at best only approximately fulfills the mathematical conditions on which precise proof is built and a physicist should be constantly aware of the approximate nature of his calculations.
In general, the Egyptians say that their ancestors sent forth numerous colonies to many parts of the inhabited world, the pre-eminence of their former kings and their excessive population; 6 but since they offer no precise proof whatsoever for these statements, and since no historian worthy of credence testifies in their support, we have not thought that their accounts merited recording.
"It's hard to believe that the U.S., with all of its spy satellites available for monitoring everything in Ukraine that precise proof of who did what and when is not available," he added.
It's unclear whether the public will demand such precise proof of safety before accepting driverless cars on the road, says Nidhi Kalra, the co-author of the Rand report.
In some cultural practices indigenous to each region, data related to the date of birth might be misleading, especially if no central registration boards or no precise proof of age exist [ 26].
However, even detailed and precise proofs are rarely expressed purely in the language of logic; rather, they are a mixture of ordinary language, mathematical, and logical symbols and terminology.
It is then possible to give a precise version and a proof of the adequacy condition (T) in a meta-science, whose principles comprise: (i) general logical axioms, (ii) special axioms that depend upon the object theory we consider, and (iii) axioms for dealing with the fundamental properties of the structural notions, i.e., principles of proof and definition by induction.
We give a substantially simpler and more direct proof in a precise manner, in comparison to Corollary 5.2 of [10].
