It is always understood that constant specifications cover axioms from the enlarged set.
For convenience in the notation and simplicity in the proofs, we suppose that functions vanish out of their specified domains, that is, let be defined for some, then it is always understood that for, where is the characteristic function of defined by for and for.
Airbus was formed in 1970 by a coalition of British, French and German companies, but has received substantial state subsidies, and it was always understood that its operations would be coordinated with the three governments' political interests; thus plants and management were spread over the three countries (though last year Britain's BAE sold its interest to Airbus' parent company, EADS).
It was always understood that you could knock next door for a bowl of sugar, some salt, an onion.
"Obviously it's a loss to say that the federal government has no right to define marriage as it's always understood," he said.
"He could be, and he can be now, tremendously gregarious," she says, "but it was always understood that he had to be out of touch for long stretches of time".
"It was always understood that there were many reasons that people were obese," said Dr. Michael First, a professor of psychiatry at Columbia and one of two editors of the association's manual, known as D.S.M.IV.
"It was always understood this would be left until after the election," says Smith, who adds that at ministerial level thinking has progressed, with proposals likely to be published shortly.
"The senior management of the bank was appointed by him, and we ratified his decisions because it was always understood that when this began in 1989, this was his bank to run and his bank to supervise".
He was going to earn $10.3 million this season whether he played or not, and it was always understood he would take the money as a buyout and not a 2003 salary.
In the latest documents, Olswang, the law firm acting for Chappell, says that it was always understood, up until a month before the sale, that BHS was to be delivered free of the deficit in its pension fund – that is the deficit that has subsequently ballooned to £571m on one accounting measure.
