We can now prove several lemmas.

In such diseases as cancer, tuberculosis, and heart disease, early diagnosis and treatment are so vital that the waste of time by the patient with Doctor Fraud's cure-all gadget can prove fatal.

Some turnpikes have not been in full operation long enough to prove what they can do.

If a defendant has been convicted and can prove that his lawyer did not adequately handle his case and that there is a reasonable probability that the result of the trial would have been different had the lawyer given competent representation, he is entitled to a new trial.

Sometimes slightly stronger theories such as Morse-Kelley set theory or set theory with a strongly inaccessible cardinal allowing the use of a Grothendieck universe are used, but in fact most mathematicians can actually prove all they need in systems weaker than ZFC, such as second-order arithmetic.

The notion of the Kolmogorov complexity can be used to state and prove impossibility results akin to Gödel's incompleteness theorem and Turing's halting problem.

Thus, intuitionists are ready to accept a statement of the form " P or Q " as true only if we can prove P or if we can prove Q:

Similarly, intuitionists object to the existence property for classical logic, where one can prove, without being able to produce any term of which holds.

* techniques and methods from one area can be applied to prove results in a related area.

These poles and zone-lines, whilst inducing fluctuations in data density in the reconstructed datasets, which can prove problematic during post-analysis, are critical for determining information such as angular magnification, as the crystallographic relationships between features are typically well known.

If these preliminary results prove successful in larger trials, then At-DBF2 genes can help in engineering crops that can better withstand harsh environments.

Many practical problems are actually " easy ", so the SAT solver can easily find a solution, or prove that none exists, relatively quickly, even though the instance has thousands of variables and tens of thousands of constraints.

One can proceed to prove theorems about groups by making logical deductions from the set of axioms.

In this fashion, one can prove many important theorems in the class of compact spaces, that do not hold in the context of non-compact ones.

The data can either be used as fingerprint to prove material identity or the GC / MS data is used to identify individual fragments to obtain structural information.

It can be much easier to show a proposition's truth to follow from another proposition than to prove it independently.

An intuitive design can prove most effective in developing the content and layout of a customer relationship management system.

The amount of time needed for the development and implementation of a customer relationship management system can prove costly to the implementation as well.

This can prove useful for users who might find themselves lost or unsure how they got to the current screen in the CRM.

Strong writing skills can prove extremely beneficial for software development and creation.

Research notes that test users can prove to be most effective in providing developers a structured overview of the software creation.

In New Zealand, where abalone is called pāua ( from the Māori language ), this can be a particularly awkward problem where the right to harvest pāua can be granted legally under Māori customary rights.

Some authors also require the domain of the Euclidean function be the entire ring R ; this can always be accommodated by adding 1 to the values at all nonzero elements, and defining the function to be 0 at the zero element of R, but the result is somewhat awkward in the case of K. The definition is sometimes generalized by allowing the Euclidean function to take its values in any well-ordered set ; this weakening does not affect the most important implications of the Euclidean property.

Holding down buttons while moving the mouse can be awkward and requires some practice, since the downwards action increases friction for the horizontal motion.

The connotations of " motel " as adult motel or love hotel in both the Spanish and Portuguese languages can be awkward for US-based chains accustomed to using the term in its original meaning, although this issue is diminishing as chains ( such as Super 8 Motels ) increasingly drop the word " motel " from their corporate identities at home.

On one hand, a 5-3 major-suit can easily be missed if it is allowed ; on the other, such hands present an awkward second-round rebid if opened 1 of a major ( especially if 1NT is in 15-18 range ).

This can happen when accessing awkward locations, or when working on cramped live circuitry.

Nightmares can have physical causes such as sleeping in an uncomfortable or awkward position, having a fever, or psychological causes such as stress and anxiety.

The original texts of Shakespeare's plays do not have cast lists, and can sometimes be inconsistent about what they call characters, but he is a particularly awkward case.

This can lead to constructions denoting an intermediate level of formality in T – V-distinct languages that sound awkward to English-speakers.

In more complicated contexts, such notations can become awkward and confusing.

This can create some awkward situations for users of distributions derived from Debian.

In very long strings of swara, the performers must calculate their notes accurately to ensure that they stick to the raga, have no awkward pauses or lapses in the beat of the song, and create a complex pattern of notes that a knowledgeable audience can follow.

The position can also be awkward for partners who are not similar in height.

This can lead to awkward or painful positions depending on how the handcuffs were applied, and typically requires a good amount of flexibility.

Combined with their body shape this can make some species awkward on land, but they are stronger walkers than other marine and water birds such as grebes or petrels.

Chronic encephalomyelitis, which may be progressive, can involve cognitive impairment, weakness in the legs, awkward gait, facial palsy, bladder problems, vertigo, and back pain.

Pursued by local lovelies Hopeful Mudd and Boyless Bailey, Tiny was even dumber and more awkward than Abner, if that can be imagined.

It can be awkward to use studded beams in vertical structures because it is necessary to insert plates between the studded beams in order to get the holes to line up.

While use case theory suggests that UI not be reflected in use cases, it can be awkward to abstract out this aspect of design, as it makes the use cases difficult to visualize.

The thermal situation for airbreathers ( particularly scramjets ) can be awkward ; normal rockets fly steep initial trajectories to avoid drag, whereas scramjets would deliberately fly through relatively thick atmosphere at high speed generating enormous heating of the airframe.

They are self-assured on the vertical surfaces of large trees but can seem awkward while feeding on small branches and vines.

While hunting on the ground, almost entirely for large insects, their gait can appear awkward but they are often successful in pinning down several insects per day.

The melody is not usually sung by the tenor or bass, except for an infrequent note or two to avoid awkward voice leading, in tags or codas, or when some appropriate embellishment can be created.

As a result of the above factors, the use of correct vocabulary to describe a given participant in this movement can occasionally be awkward, confusing, or controversial.