Sentence examples for explicit proofs of from inspiring English sources

Direct and explicit proofs of the influence of al-Ghazali on Medieval Jewish philosophy appeared in Spain and Provence from 1270 onwards.

Outright bribery requires explicit proof of a quid pro quo, which is often difficult to get.

Bush's crooked Justice Department prosecutors wrongfully prevailed upon a Reagan-appointed judge to withhold that instruction and to allow Minor's conviction without the explicit proof of a quid pro quo.

We then give explicit proof of a stronger version of Remark 2.9 from Sauer et al. [29] that allows non-consecutive lags.

In the study, we also provided explicit proofs to convince more members in the miRNA world.

There are few mouthpieces for the prosecution and although the viewer is left with a sense that this was a vendetta of some kind, there is no explicit proof to that effect.

Unfortunately, Gödel's work (Gödel 1938) remained unpublished until 1995, by which time the Gödelian logic of explicit proofs had already been rediscovered, and axiomatized as the Logic of Proofs \(\mathsf{LP}\) and supplied with completeness theorems connecting it to both \(\mathsf{S4}\) and classical proofs (Artemov 1995).

The situation after (Gödel 1933) can be described by the following figure where '\(X \hookrightarrow Y\)' should be read as '\(X\) is interpreted in \(Y\)' In a public lecture in Vienna in 1938, Gödel observed that using the format of explicit proofs: can help in interpreting his provability calculus \(\mathsf{S4}\) (Gödel 1938).

British regulators have said that they did not have explicit proof then of wrongdoing by banks.

As part of a project to provide a constructive semantics for intuitionistic logic, a formal logic of explicit proof terms was presented in Artemov 2001.

Therefore genome G is the solution of the Breakpoint Median Problem on P, Q and R. ▪ Assuming the Breakpoint Median Problem for four genomes L, P, Q and R were also NP-hard, although we are not aware of any explicit proof, we could use the same method employed above to show that GGH with two outgroups is hard under the d B distance.