Then the theory at hand, which is assumed to prove certain facts about numbers, also proves facts about its own statements.

Then the theory at hand, which is assumed to prove certain facts about numbers, also proves facts about its own statements, provided that it is effectively generated.

Then we could equate F < sub > E </ sub > with w. Also, determining F < sub > E </ sub > proves difficult because the mass of the oil drop is difficult to determine without reverting back to the use of Stokes ' Law.

Then one proves that if the theorem is true for pieces resulting from a cutting of a Haken manifold, that it is true for that Haken manifold.

Then, if the logical negation is used as the antithesis, there is no rigorous way to derive a synthesis.

Then he thought of a time when Clayton's horse had fallen lame in the Gap.

Then, and only then, with the Jacksons and Dan as their true guests of honor, did the Harrows take time to catch up on the news.

Then maybe next time he won't be so quick on the trigger ''.

Then, to conclude on an indeterminate note: `` Nevertheless, if fallout increased substantially, or remained high for a long time, it would become far more important as a potential health hazard in this country and throughout the world ''.

Then, for the first time since his arrest, a glint of spirit lit Barco's eyes.

Then I realized that she had been deliberately showing me, this time, what Granny was like ; ;

Then comes the time when the last wire is removed and Susie walks out a healthier and more attractive girl than when she first went to the orthodontist.

Then on Monday morning -- or it might have to be Tuesday -- get up and leave just the usual time, and last thing, put the money in an envelope under the old woman's purse there in the drawer.

Then we can express the variables as the sum of the ( time averaged ) mean field () that varies in space and a small fluctuating field () that varies in space and time.

Then, following the programme he outlined in his talk at the 1958 International Congress of Mathematicians, he introduced the theory of schemes, developing it in detail in his Éléments de géométrie algébrique ( EGA ) and providing the new more flexible and general foundations for algebraic geometry that has been adopted in the field since that time.

) Then X < sub > i </ sub > is the value ( or realization ) produced by a given run of the process at time i. Suppose that the process is further known to have defined values for mean μ < sub > i </ sub > and variance σ < sub > i </ sub >< sup > 2 </ sup > for all times i. Then the definition of the autocorrelation between times s and t is

Then, in the time of Pope Gregory VII ( 1073 – 1085 ), canonists who in the Investiture Controversy quoted the prohibition in canon 22 of the Council of Constantinople of 869 – 870 against laymen influencing the appointment of prelates elevated this council to the rank of ecumenical council.

Then in 794 Kammu suddenly shifted the capital again, this time to Heian-kyō, which is modern day Kyoto.

Then followed the time of the Arian controversies, and dogmatic questions came into the foreground.

Then the tumult of the thousand different cries of the eager dealers, all shouting at the top of their voices, at one and the same time, is almost bewildering.

Then Marlow and his listeners were silent ; our first narrator explains: " Nobody moved for a time.

Then, only time and the component in the direction of v ;

For example, resurrection of the dead, which is exegetically supported by a verse in Exodus 15: " Az Yashir Moshe ..."-" Then will sing ...", from which is derived that " then " ( in the Messianic Era ) Moses will arise and once again sing as he did at the time of the Exodus.

Then, five pages later, she quotes the same passage again, but this time in full, straw and all, to show how witches had hallucinations of flight ( Murray 1921, 105-6 ); she does not realise that she has thereby wrecked her previous rationalistic interpretation of the passage.

My own stern hand has rent the ancient bond, And thereof shall the ending not have end: But not for me, that loved her, to be fond Lightly to please me with a newer friend Then hold it more than bravest-feathered song, That I affirm to thee, with heart of pride, I knew not what did to a friend belong Till I stood up, true friend, by thy true side ; ;

Then in 2 we show that any line involution with the properties that ( A ) It has no complex of invariant lines, and ( B ) Its singular lines form a complex consisting exclusively of the lines which meet a twisted curve, is necessarily of the type discussed in 1.

`` Then see that your youngster has a routine checkup once a year ''.

Then it turns out that the child has constructed this elaborate ruse in order to steal cookies and watch late-night TV without notice, giving him ur-manipulator status.

Then on July 20, 2007 guitarist Jack Owen ( ex-Cannibal Corpse ) announced that Deicide is " on hiatus " and he has joined Ohio based death / thrash combo Estuary for touring purposes.

Then, dividing the units of energy ( such as eV ) by a fundamental constant that has units of velocity ( M < sup > 0 </ sup > L < sup > 1 </ sup > T < sup >-1 </ sup >), facilitates the required conversion of using energy units to describe momentum.

Then he announced to the world: " The independence of Austria, for which he has fallen, is a principle that has been defended and will be defended by Italy even more strenuously ", and then replaced in the main square of Bolzano the statue of Walther von der Vogelweide, a Germanic troubadour, with that of Drusus, a Roman general who conquered part of Germany.

" Then examine it and test it by these rules you have, and firstly, and chiefly, by this: whether the impression has to do with the things that are up to us, or those that are not ; and if it has to do with the things that are not up to us, be ready to reply, " It is nothing to me.

Then, after the synthesis engine has mapped the design to a netlist, the netlist is translated to a gate level description where simulation is repeated to confirm the synthesis proceeded without errors.

Then he said " I'm fining everyone in this courtroom fifty cents for living in a city where a person has to steal bread in order to eat!

Then, Gödel defined essences: if x is an object in some world, then the property P is said to be an essence of x if P ( x ) is true in that world and if P entails all other properties that x has in that world.

Then Scarlett meets Rhett Butler, a man who has a reputation as a rogue.

Then, the intended recipient ( B ), who also has been informed by A about the password ( 2a ), now approaches M and tells him the agreed password ( 3a ).

Then a general definition of isomorphism that covers the previous and many other cases is: an isomorphism is a morphism that has an inverse, i. e. there exists a morphism with and.

“ And that Christ being Lord, and God the Son of God, and appearing formerly in power as Man, and Angel, and in the glory of fire as at the bush, so also was manifested at the judgment executed on Sodom, has been demonstrated fully by what has been said .” Then I repeated once more all that I had previously quoted from Exodus, about the vision in the bush, and the naming of Joshua ( Jesus ), and continued: “ And do not suppose, sirs, that I am speaking superfluously when I repeat these words frequently: but it is because I know that some wish to anticipate these remarks, and to say that the power sent from the Father of all which appeared to Moses, or to Abraham, or to Jacob, is called an Angel because He came to men ( for by Him the commands of the Father have been proclaimed to men ); is called Glory, because He appears in a vision sometimes that cannot be borne ; is called a Man, and a human being, because He appears arrayed in such forms as the Father pleases ; and they call Him the Word, because He carries tidings from the Father to men: but maintain that this power is indivisible and inseparable from the Father, just as they say that the light of the sun on earth is indivisible and inseparable from the sun in the heavens ; as when it sinks, the light sinks along with it ; so the Father, when He chooses, say they, causes His power to spring forth, and when He chooses, He makes it return to Himself.

Then, after the pump energy stored in the laser medium has approached the maximum possible level, the introduced loss mechanism ( often an electro-or acousto-optical element ) is rapidly removed ( or that occurs by itself in a passive device ), allowing lasing to begin which rapidly obtains the stored energy in the gain medium.

Then the null set automatically has measure zero because of countable additivity, because and is finite if and only if the empty set has measure zero.

Then the scene shifts: Odysseus has been a captive of the beautiful nymph Calypso, with whom he has spent seven of his ten lost years.