Sentence examples for to construct a proof of from inspiring English sources
In order to work constructively, we need to re-interpret not only the existential quantifier but all the logical connectives and quantifiers as instructions on how to construct a proof of the statement involving these logical expressions.
But, by the Pythagorean theorem, a2 + b2 = c2, so A + B = C. Conversely, if we can prove that A + B = C for three similar figures without using the Pythagorean theorem, then we can work backwards to construct a proof of the theorem.
Our next goal was to construct a proof-of-concept of a biologically meaningful classification of the interaction interfaces, using the feature-based similarity measure.
"These discoveries cannot, in themselves, be used to construct a formal proof of the existence of God, but they do evoke a sense of wonder to which a religious response is natural," he says.
Decidability means that at present for any given $n$ there exists (can be constructed) a proof of $A(n)$ or of $\neg A(n)$.
However within the framework of Justification Logic, building on the proofs of \(X\) and of \(X\leftrightarrow Y\), we can construct a proof term \(f u,v)\) which represents the proof of \(Y\) and so \(f u,v Y\) is provable.
After reducing the system to its parts, the next step in the standard approach to understanding, according to Kellert, is to construct a "deductive scheme, which yields a rigorous proof of the necessity (or expectability) of the situation at hand" (1993, p. 91).
The crucial part of the proof is to construct a delayed likelihood ratio depending on a parameter, and then applies the Borel-Cantelli lemma.
While NK constructs an actual proof (of the conclusion from the given assumptions), LK instead constructs a proof that proves the existence of a proof (of the conclusion from the assumptions).
Notably, the nonsense shRNAs and a reported efficient sgRNA targeting the mouse p53 gene (sgp53) (Xue et al., 2014) was adopted in the construct for a proof-of-concept experiment.
