Sentence examples for direct proofs for from inspiring English sources

New (direct) proofs for some criteria are provided.

In contrast with [23], we give a direct proofs for the continuity and compactness of F and G without using a continuity result on superposition operators.

According to Hafner, Bolzano prefers direct proofs for two reasons: 1) indirect proofs proceed by a detour [Umweg] and contain redundant premises, 2) indirect proofs always contain a false premise which cannot be admitted as the ground of other truths.

These liftings provide direct proofs for the classical theorems of Sarason and of Sz.-Nagy and Foias, as well as a bidimensional version of Sarason′s theorem, and a theorem of Sz.-Nagy-Foias type for two pairs of dilations.

Recently, Zhou and his collaborators [7] give a direct proof for McKean's theorem [5].

This is a direct proof for less oxygen content for the upper layers of the thicker film.

This is additionally supported by EDAX analysis which provides the direct proof for the adsorption of fluoride ions onto AHAC.

We give a direct proof for the following useful lemma, which can also be deduced from Theorem 2.3.9 in [24].

Although Suddendorf finds the team's interpretations "sensible" and "plausible," he cautions that the experimental results cannot be considered direct proof for the theory behind them.

Furthermore, the marked area highlighted the opened CNT tips, which provides a direct proof for the opening of the exposed CNTs by oxidative plasma.

We are aware that the present analyses were based on taxonomic abundance data only and thus are no direct proof for pyrene degradation activity by theses genera.