Then the various officers of the college might take up the case.

Then it was that District Attorney Welch entered the case.

Then, when the case went to the jury, the judge excused one of the jurors, saying the juror had told him he had been accosted by masked men at his motel the night before the trial opened.

Then, when Macbeth approaches, Banquo, having had dreams about Macbeth's deeds, takes back his sword as a precaution in this case.

Then one must extract the principles, analogies and statements by various courts of what they consider important to determine how the next court is likely to rule on the facts of the present case.

Indeed, following, suppose ƒ is a complex function defined in an open set Ω ⊂ C. Then, writing for every z ∈ Ω, one can also regard Ω as an open subset of R < sup > 2 </ sup >, and ƒ as a function of two real variables x and y, which maps Ω ⊂ R < sup > 2 </ sup > to C. We consider the Cauchy – Riemann equations at z = 0 assuming ƒ ( z ) = 0, just for notational simplicity – the proof is identical in general case.

Then Fick's first law ( one-dimensional case ) can be written as:

Then, once this claim ( expressed in the previous sentence ) is proved, it will suffice to prove " φ is either refutable or satisfiable " only for φ's belonging to the class C. Note also that if φ is provably equivalent to ψ ( i. e., ( φ ≡ ψ ) is provable ), then it is indeed the case that " ψ is either refutable or satisfiable " → " φ is either refutable or satisfiable " ( the soundness theorem is needed to show this ).

#* Proof: Then so Thus However, is prime, so or In the former case, hence ( which is a contradiction, as neither 1 nor 0 is prime ) or In the latter case, or If however, which is not prime.

Then the first case of Fermat's Last Theorem holds true for p.

⟨ H ⟩, be the group generated by H. Then the word problem in H < sup >*</ sup > is solvable: given two words h, k in the generators H of H < sup >*</ sup >, write them as words in X and compare them using the solution to the word problem in G. It is easy to think that this demonstrates a uniform solution the word problem for the class K ( say ) of finitely generated groups that can be embedded in G. If this were the case the non-existence of a universal solvable word problem group would follow easily from Boone-Rogers.

Then the question being whether legislative interference was required I was at length induced to look at a remedy of an extraordinary character as the only one I thought applicable to the case ... it was a great innovation ".

Then she shows him a long, narrow case, which she tells him holds her only sacred treasure, but she cannot open it, because there are too many people around.

Then consider the case of American immigration.

The incident, like others in Matthew, is described as the fulfillment of a passage in the Old Testament read as prophecy, in this case a reading of Jeremiah: " Then was fulfilled that which was spoken through Jeremiah the prophet, saying, A voice was heard in Ramah, Weeping and great mourning, Rachel weeping for her children.

Then he threw the lid of the case to a placed called Guneshwara ( now Gunavanthe ) and Dhareshwara, 10 – 12 miles away.

In this case we can write the eigenvalues as Then it can be shown that can be rewritten as

Then gcd ( a < sup > e </ sup > − 1, n ) is likely to produce a factor of n. However, the algorithm fails when p-1 has large prime factors, as is the case for numbers containing strong primes, for example.

Then a C-valued presheaf on X is the same as a contravariant functor from O ( X ) to C. This definition can be generalized to the case when the source category is not of the form O ( X ) for any X ; see presheaf ( category theory ).

Then though Gettier's cases stipulate that Smith has a certain belief and that his belief is true, it seems that in order to propose ( 1 ), one must argue that Gettier, ( or, that is, the writer responsible for the particular form of words on this present occasion known as case ( 1 ), and who makes assertion's about Smith's " putative " beliefs ), goes wrong because he has the wrong notion of justification.

Then for an equation to have a solution, we must have ( one constraint ), and in that case the solution space is or equivalently stated, ( one degree of freedom ).

" Then the band " changed the letter so that we wouldn't find a band with the same name again like it was the case with Crystaline Darkness.

Then this can be seen by a direct computation for n any integer, and the general case reduces to this case without much difficulty.

Then he would get to his feet, as though rising in honor of his own remarkable powers, and say almost invariably, `` Gentlemen, this is an amazing story!!

Then, Jesus indicated that God's forgiveness is unlimited.

Certainly, the meaning is clearer to one who is not familiar with Biblical teachings, in the New English Bible which reads: `` Then Jesus arrived at Jordan from Galilee, and he came to John to be baptized by him.

Then it added: `` It is not possible to determine how extensive these ill effects will be -- nor how many people will be affected ''.

Then the words fell into a pattern: `` Mollie the Mutton is scratching her nose, Scratching her nose in the rain.

Then he thought of Aaron Blaustein standing in his rich house saying: `` God is tired of taking the blame.

Then it is marked on the inside where it comes in contact with the transom, frames, keelson and all the battens.

Then it is replaced and fastened.

Then the chines are rounded off and the bottom is rough-sanded in preparation.

Then, a group of eggs is deposited in a cavity in the beebread loaf and the egg compartment is closed.

Then there is a diagonalizable operator D on V and a nilpotent operator N in V such that ( A ) Af, ( b ) Af.

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, too, the utmost clinical flexibility is necessary in judiciously combining carefully timed family-oriented home visits, single and group office interviews, and appropriate telephone follow-up calls, if the worker is to be genuinely accessible and if the predicted unhealthy outcome is to be actually averted in accordance with the principles of preventive intervention.

Then the editorial added prophetically: `` how far they may reach in Asia is yet undetermined, but they fall far short of our dreams of the war conferences ''.

Then she catapults into `` everything and everybody '', putting particular violence on `` everybody '', indicating to the linguist that this is a spot to flag -- that is, it is not congruent to the patient's general style of speech up to this point.

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, with the new affluence, there is actually a sallying forth into the wide, wide world beyond the precincts of New York.

Then, if the middle number is activated to its greatest potential in terms of this square, through multiplying it by the highest number, 9 ( which is the square of the base number ), the result is 45 ; ;