::( P ( 0 ) ∧ ∀ x ( P ( x ) → P ( x + 1 ))) → ∀ y P ( y ).

::( q < sub > 1 </ sub >, w, x < sub > 1 </ sub >) ( p < sub > 1 </ sub >, )

::( p < sub > 1 </ sub >,, x < sub > 2 </ sub >) ( p < sub > 2 </ sub >, )

::( p < sub > m </ sub >,, ) ( p < sub > m + 1 </ sub >, y < sub > n </ sub >)

::( p < sub > m + 1 </ sub >,, ) ( p < sub > m + 2 </ sub >, y < sub > n-1 </ sub >)

::( p < sub > m + n-1 </ sub >,, ) ( q < sub > 2 </ sub >, y < sub > 1 </ sub >)

::( 1 ) If, by reason of death, resignation, removal from office, inability, or failure to qualify, there is neither a President nor Vice President to discharge the powers and duties of the office of President, then the Speaker of the House of Representatives shall, upon his resignation as Speaker and as Representative in Congress, act as President.

::( 1 ) if his discharge of the powers and duties of the office is founded in whole or in part on the failure of both the President-elect and the Vice-President-elect to qualify, then he shall act only until a President or Vice President qualifies ; and

::( 1 ) If, by reason of death, resignation, removal from office, inability, or failure to qualify, there is no President pro tempore to act as President under subsection ( b ) of this section, then the officer of the United States who is highest on the following list, and who is not under disability to discharge the powers and duties of the office of President shall act as President: Secretary of State, Secretary of the Treasury, Secretary of Defense, Attorney General, Secretary of the Interior, Secretary of Agriculture, Secretary of Commerce, Secretary of Labor, Secretary of Health and Human Services, Secretary of Housing and Urban Development, Secretary of Transportation, Secretary of Energy, Secretary of Education, Secretary of Veterans Affairs, Secretary of Homeland Security.

::( 2 ) An individual acting as President under this subsection shall continue so to do until the expiration of the then current Presidential term, but not after a qualified and prior-entitled individual is able to act, except that the removal of the disability of an individual higher on the list contained in paragraph ( 1 ) of this subsection or the ability to qualify on the part of an individual higher on such list shall not terminate his service.

::( 3 ) The taking of the oath of office by an individual specified in the list in paragraph ( 1 ) of this subsection shall be held to constitute his resignation from the office by virtue of the holding of which he qualifies to act as President.

::( 1, 5 ) ( 2, 5 ) ( 3, 5 )

::( 1, 4 ) ( 2, 4 ) ( 3, 4 )

::( 1, 3 ) ( 2, 3 ) ( 3, 3 )

::( 1 ) In this Act " terrorism " means the use or threat of action where -

::( 3 ) The use or threat of action falling within subsection ( 2 ) which involves the use of firearms or explosives is terrorism whether or not subsection ( 1 )( b ) is satisfied.

::( 1 ) Engages in fighting or other violent conduct or in conduct creating the threat of imminent fighting or violence ; or

::( 1 ) intentionally or knowingly:

::( 1 ) entering or taking anything in his dwelling ;

::( 1 ) to perform or display it at a place open to the public or at any place where a substantial number of persons outside of a normal circle of a family and its social acquaintances is gathered ; or

::( 2 ) to transmit or otherwise communicate a performance or display of the work to a place specified by clause ( 1 ) or to the public, by means of any device or process, whether the members of the public capable of receiving the performance or display receive it in the same place or in separate places and at the same time or at different times.

::( 2Cyl ) < math > x ^ 2 + y ^ 2 < 1

::( a ) The official scorer shall credit a batter with a base hit when:

::( Rejoice and sing, France: the lily is bathed with heavenly dew.

::( ii ) The space of continuous real-valued functions on X with the supremum norm is separable.

::( e ) engages in conduct that assists by any means whatever, with intent to assist, an enemy:

::( f ) engages in conduct that assists by any means whatever, with intent to assist:

::( 2 ) with intent to cause the overthrow or destruction of lawful civil authority, creates, in concert with any other person, revolt, violence, or other disturbance against that authority is guilty of sedition ;

::( In this art, scenes from nature, human activities, and all other real world phenomena will not be described for their own sake ; here, they are perceptible surfaces created to represent their esoteric affinities with the primordial Ideals.

::( ii ) A person duly attached or lent as a non-commissioned officer to or seconded for service or appointed for duty as a non-commissioned officer with the Navy:

::( ii ) A person duly attached or lent as a non-commissioned officer to or seconded for service or appointed for duty as a non-commissioned officer with the Army:

::( ii ) A person duly attached or lent as a non-commissioned officer to or seconded for service or appointed for duty as a non-commissioned officer with the Air Force :" – Defence Act 1990, Sect 2 ( Interpretation )

::( ii ) with intent to engage in conduct constituting a violation of section 7201 or 7206 of the Internal Revenue Code of 1986 ; or

::( a ) they are to be of the greatest benefit of the least-advantaged members of society, consistent with the just savings principle ( the difference principle ).

::( a ) to the greatest benefit of the least advantaged, consistent with the just savings principle, and

::( includes list of people with this name )

::( g ) being disqualified under any law relating to offences in connection with elections to Parliament or the office of President by reason of having been convicted of such an offence or having in proceedings relating to such an election been proved guilty of an act constituting such an offence.

::( d ) Restricted capacity of the individual's brain which can lead to excessive specialization, with consequent dangers of degeneration.

::( with his tongue in his cheek )

::( 3 ) of any woman with respect to her unborn child.

::( d ) the electronic signature can be linked with an electronic document in such a way that it can be used to determine whether the electronic document has been changed since the electronic signature was incorporated in, attached to or associated with the electronic document.

::( b ) To use or employ, in connection with the purchase or sale of any security registered on a national securities exchange or any security not so registered, or any securities-based swap agreement ( as defined in section 206B of the Gramm-Leach-Bliley Act ), any manipulative or deceptive device or contrivance in contravention of such rules and regulations as the Commission may prescribe as necessary or appropriate in the public interest or for the protection of investors.

::( As a counterexample, if one does not assume continuity or measurability, it is possible to prove the existence of an everywhere-discontinuous, non-measurable function with this property by using a Hamel basis for the real numbers over the rationals, as described in Hewitt and Stromberg.