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Thus and requires
Thus Christ's atonement is intended for all, but requires faith to be effected.
Thus, though knowledge requires justification, truth, and belief, the word " knowledge " can't be, according to Williamson's theory, accurately regarded as simply shorthand for " justified true belief.
Thus, a solution requires that no two queens share the same row, column, or diagonal.
Thus for a large or very distributed company that requires multiple PBXs, users can receive the same services across the network and be unaware of the switch that their telephone is connected to.
Thus, as per Draper's argument above, the theory that there is an omniscient and omnipotent being who is indifferent requires no hidden reasons in order to explain evil.
Thus for finite n, the expression " n-th element " of a well-ordered set requires context to know whether this counts from zero or one.
Thus, assigning age significance to a result requires studying the metasomatic and thermal history of the rock, any metamorphic events, and any evidence of fluid movement.
Thus, the work requires great strength and is quite hazardous to the back, hands, and feet.
Thus Real Alternative requires RealPlayer to be installed ( or at least its DLLs ) in order to function.
Thus, the basis of morality is strong moral character, which requires self-reliance and self-discipline.
Thus an eye care professional, having determined that a myopic ( nearsighted ) person requires a basic correction of, say, − 2 dioptres to restore normal distance vision, might then make a further prescription of ' add 1 ' for reading, to make up for lack of accommodation ( ability to alter focus ).
Thus, a neutral point of view requires testing measures consensual to anyone expected to believe the results.
Thus, any real approach to modeling landscapes requires the ability to modulate fractal behaviour spatially.
Thus compatibility with data in the old format may need to be kept when switching to a different format, even when decoding from ( as with many MPEG formats ), or distribution in ( as has at least been planned with H. 264 ) the old format requires paying royalties.
Thus, if one of the coordinates, say q < sub > k </ sub >, does not appear in the Lagrangian, the right-hand side of the equation is zero, and the left-hand side requires that
Thus creating a fireball requires the following formula: Create Fire.
Thus, attempts to define electrochemical potential in this way cannot lead to the kind of universal parameter that thermodynamics ideally requires.
Thus, lighting a larger area to the same level of lux requires a greater number of lumens.
Thus, x86 instructions that operate on the memory ( e. g., add this register to this location in the memory ) can only be processed by the general decoder, as this operation requires at a minimum of three micro-ops.
Thus, large stitches can be made with large needles, whereas fine knitting requires fine needles.
Thus, the sustainable management requires finding out what business activities fit into the Earth ’ s carrying capacity, and also defining the optimal levels of those activities.
Thus usually requires the rider to be pedalling, but some systems have been developed with the freewheel in the crankset so that the chain moves even when the rider is not pedalling.
Thus, on an additive white Gaussian noise ( AWGN ) channel without interference, a spread system requires the same transmitter power as an unspread system, all other things being equal.
Thus using a computer in the digital production of caricatures requires advanced knowledge of the program's functionality.

Thus and sufficient
Thus, by the end of 1992, Azerbaijan received arms and military hardware sufficient for approximately four motor rifle divisions with prescribed army units.
Thus, after a bid of 3, bids of 2 or 3 are not sufficient, but 3 or 4 are.
Thus the necessary and sufficient conditions for the truth of a proposition of law simply involved internal logic and consistency, and that the state's agents used state power with responsibility.
Thus mail armour proved to be sufficient protection in most situations.
Thus, the attack on the Soviet Union ( which together with Germany had partitioned central Europe in 1939 – 1940 ) was not pressed with sufficient strength.
Thus, a unique trajectory in the thunderstorm is sufficient to explain the layer-like structure of the hailstone.
Thus, these cells cannot survive for long ' as they cannot exchange sufficient material to maintain active metabolism.
Thus shot noise is more frequently observed with small currents or light intensities following sufficient amplification.
Thus, she concluded, phonics instruction is a necessary component of reading instruction, but not sufficient by itself to teach children to read.
Thus over months-to-years, the net ( integrated ) amount of force is substantial, and is thought to be sufficient to speed interplanetary probes to velocities that could traverse the Earth-Pluto distance in 1 / 2 to 1 / 4 the time of a chemically accelerated vessel.
Thus, to abduce from involves determining that is sufficient ( or nearly sufficient ), but not necessary, for.
Thus the full dictionary does not need be sent with the encoded data ; just the initial dictionary containing the single-character strings is sufficient ( and is typically defined beforehand within the encoder and decoder rather than being explicitly sent with the encoded data.
Thus, for the human wave attack to succeed on the modern battlefield, it is imperative for the attackers to charge into the enemy line in the shortest time and in the greatest numbers possible, so that a sufficient mass can be preserved when the attackers reach melee range.
Thus, “ firewalls ” sufficient to prevent a bank from assisting its affiliate would eliminate the purpose of the combination, but “ workable ” firewalls would be insufficient to prevent such assistance.
Thus the Riksdag held the purse ; and this seemed a sufficient guarantee both of its independence and its frequent convention.
Thus in classical analysis, which uses classical logic, in order to prove the full IVT, it is sufficient to prove the constructive version.
Thus, although the typical set is loosely defined, practical notions arise concerning sufficient typicality.
Thus a screening exam is not intended to be definitive: It is intended to have sufficient sensitivity to detect a useful proportion of cancers.
Thus formalistic logic would tend to work well with the Aristotelian logic of definition by closed sets of necessary and sufficient conditions, yet is deficient when applied to areas where definition by " family resemblance " ( Wittgenstein ) is more suitable.
Thus, the commander is a double-edged sword, being able to build units and structures quickly, but at rates that quickly become unsustainable in the early game without sufficient reserves.
Thus, for exponential families, there exists a sufficient statistic whose dimension equals the number of parameters to be estimated.
Thus, whereas people may have sufficient funds to participate in some markets, their funds are inadequate to participate in other markets.
Thus, an explosive booster is used to deliver sufficient shockwave to the main charge.

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