Brouwer's proof of the bar theorem from 1924 (later versions of the proof appeared in 1927 and in 1954) proves a statement of the form "If A has been demonstrated, then B is demonstrable" (Brouwer 1924D1, Brouwer 1927B, Brouwer 1954A).
"There will be lots of public support for it, it will create demonstrable cost-savings, and it's great for the American businesses that are making a business of helping others save energy".
A breakdown over the issue has serious implications for David Cameron's strategy on Europe as this is one of the main issues he was hoping to secure demonstrable progress on this side of the general election, regardless of any promises of a referendum afterwards.
There is no demonstrable data to prove that.
And in a few other countries, notably Germany, Snowden's revelations do seem to be having a demonstrable impact – as witnessed, for example, by the Bundestag's inquiry into NSA surveillance within the Federal Republic.
He also has a habit of telling demonstrable lies, such as his claim that the Russian troops in Crimea are not in fact Russian troops.
The Gates Foundation has an obsession with achieving demonstrable change with its money.The new campaign comes at an interesting time for the rich in America.
Teachers will now find it more difficult to get tenure, as well they should; instead of coming after three years in the classroom it will now take at least five, and it will take demonstrable results too.
Any demonstrable harm caused by the use of plastics and painkillers has to be weighed against the benefits they bring, such as reliability and efficacy.
China's execution of these conditions would be a demonstrable movement towards improving its human rights situation.It is important to realize that the world community presently holds the upper hand with respect to China's integration with the world community.
Planned Parenthood is fundamentally a women's-health organisation, not a political combatant, despite what you hear from some segments of the right; and Komen is a charity with an interest in women's health.One aspect of this that I think is worth flagging is that it is the second time in two weeks that vocally upset people have had a demonstrable effect on an issue.
