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In type 1 the pulmonary vein closely follows the course of the bronchus and the pulmonary artery from the periphery to the hilum.

The specificity of staining with Af was established as follows: Af specifically stained tumor sections but not sections of healthy sweet clover stems or of crown gall tumor tissue from sweet clover.

It was assumed that the shift in autonomic hypothalamic balance occurring spontaneously in neuropsychiatric patients from the application of certain therapeutic procedures follows the pattern known from the sleep-wakefulness cycle.

It then follows that Af is large enough, but this is not obvious from the above expression.

The fact that there can not be any limit points of the set except in closed intervals follows from the argument used in Lemma 1, namely, that near any tangent point in the C-plane the curves C and Af are analytic, and therefore the difference between them must be a monotone function in some neighborhood on either side of the tangent point.

Since the complex of singular lines is of order K and since there is no complex of invariant lines, it follows from the formula Af that the order of the involution is Af.

A final class of exceptional lines is identifiable from the following considerations: Since no two generators of Af can intersect, it follows that their image curves can have no free intersections.

Consider what follows from the positivist view.

Our staff man cabled from Turin as follows --

The configuration of these electrons follows from the principles of quantum mechanics.

For finite sets X, the axiom of choice follows from the other axioms of set theory.

And the axiom of global choice follows from the axiom of limitation of size.

This belief follows the theology of St. Paul: For it is by grace you have been saved, through faith — and this not from yourselves, it is the gift of God, not by works, so that no one can boast.

Although Dirac did not himself use the term antimatter, its use follows on naturally enough from antielectrons, antiprotons, etc.

For Hume, every effect only follows its cause arbitrarily — they are entirely distinct from one another.

The book of Acts follows just the opposite motion, taking the scene from Jerusalem ( chs.

The distance formula on the plane follows from the Pythagorean theorem.

Today, Methodism follows this ancient Alexandrian practice as bishops are elected from and by the order of the presbyterate: the Discipline of the Methodist Church, in ¶ 303, affirms that " ordination to this ministry is a gift from God to the Church.

This conservation law mathematically follows from continuous directional symmetry of space ( no direction in space is any different from any other direction ).

The debate might be framed starkly as follows: on the one hand, we can hypothesise a poem put together from various tales concerning the hero ( the Grendel episode, the Grendel's mother story, and the firedrake narrative ).

Since a maximal ideal in A is closed, is a Banach algebra that is a field, and it follows from the Gelfand-Mazur theorem that there is a bijection between the set of all maximal ideals of A and the set Δ ( A ) of all nonzero homomorphisms from A to C. The set Δ ( A ) is called the " structure space " or " character space " of A, and its members " characters.

This follows from the Heine – Borel theorem.

Then is a compact topological space ; this follows from the Tychonoff theorem.

In Euclid's original approach, the Pythagorean theorem follows from Euclid's axioms.

It is deduced from the model existence theorem as follows: if there is no formal proof of a formula then adding its negation to the axioms gives a consisten theory, which has thus a model, so that the formula is not a semantic consequence of the initial theory.

The theorem follows because * is ( commutative and ) associative, and 1 * μ = i, where i is the identity function for the Dirichlet convolution, taking values i ( 1 )= 1, i ( n )= 0 for all n > 1.

The theorem follows by induction on the length of the game from these two lemmas.

from which the strategy above follows by the Sprague – Grundy theorem.

There is a classical analogue to the quantum no-cloning theorem, which we might state as follows: given only the result of one flip of a ( possibly biased ) coin, we cannot simulate a second, independent toss of the same coin.

This follows from the Chinese remainder theorem.

Another way of stating Rice's theorem that is more useful in computability theory follows.

* It follows easily from the Weierstrass approximation theorem that the set Q of polynomials with rational coefficients is a countable dense subset of the space C () of continuous functions on the unit interval with the metric of uniform convergence.

At any given x, a right-angled triangle connects x, y and r to the origin, hence it follows from the Pythagorean theorem that:

The statement of the approximation theorem as originally discovered by Weierstrass is as follows:

This follows from the Chinese remainder theorem and the fact that a ring of the form Z / kZ is a field if and only if k is a prime.

If both a 0 % rate and 100 % rate of taxation generate no revenue, it follows from the extreme value theorem that there must exist at least one rate in between where tax revenue would be a maximum.

It follows from the work-energy theorem that W also represents the change in the rotational kinetic energy E < sub > r </ sub > of the body, given by

* A corollary is a proposition that follows with little or no proof from one other theorem or definition.

A theorem and its proof are typically laid out as follows:

In the case that y < sub > i </ sub > are independent observations from a normal distribution, Cochran's theorem shows that s < sup > 2 </ sup > follows a scaled chi-squared distribution:

The well ordering theorem follows easily from Zorn's Lemma.

The first follows from direct diagonalization ( the space hierarchy theorem, ) and the fact that via Savitch's theorem.