Sentence examples for proof is offered from inspiring English sources
A proof is offered for the equivalence of the group velocity and the energy velocity for elastic waves in a free anisotropic homogenous plate.
It is significant that all the charges stem from unnamed sources purported to be present or former U.S. officials, but no evidence, no proof is offered in any instance.
Ordinarily a police regulation, general in operation, will not be held void as to a particular property, although proof is offered that owing to conditions peculiar to it the restriction could not reasonably be applied.
A mathematical proof is offered that the optimization problem is convex with well-known analytical conditions (specifically, KarushKuhnTucker conditions).
Once particular attention is given to implicational opacity our inability to see, before a proof is offered, the consequences of various mathematical statements much of the alleged surprise in the successful application of mathematics should vanish.
In the De probationibus the conclusion is drawn that a uniformly accelerated body will, in the second equal time interval, traverse three times the distance it does in the first, though this is only in the consideration of a particular case, and no general proof is offered.
But no proof was offered.For Mr Putin, Chechnya has become a personal crusade.
In 33.7 percent of the cases in which some proof was offered, the tree's compiler had simply cited someone else's undocumented tree.
But no proof was offered, and, except for two affirmations in radio interviews that he was heterosexual, he responded to the rumors with silence or a rebuke.
The girls in all three schools described a strange smell before they fell ill, but no scientific proof was offered that their symptoms were caused by anything they ingested or inhaled.
According to Dr. Marshall, the encyclical's assertion that it is not given to man to separate the procreative and the unitive aspects of the act of intercourse is "simply made without any proof being offered".
