Derivation Rules and Justification. The Simple Rules mA nB oA & Bn, m &I mA & B nAn &E oBn &E mA B...

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Derivation Rules and Justification

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Transcript of Derivation Rules and Justification. The Simple Rules mA nB oA & Bn, m &I mA & B nAn &E oBn &E mA B...

Page 1: Derivation Rules and Justification. The Simple Rules mA nB oA & Bn, m &I mA & B nAn &E oBn &E mA B nA oBm,n E mA B nB oAm,n E pBm,o E mA nA.

Derivation Rules and Justification

Page 2: Derivation Rules and Justification. The Simple Rules mA nB oA & Bn, m &I mA & B nAn &E oBn &E mA B nA oBm,n E mA B nB oAm,n E pBm,o E mA nA.

The Simple Rules

m An Bo A & B n, m &I

m A & Bn A n &Eo B n &E

m A Bn Ao B m,n E

m A Bn Bo A m,n Ep B m,o E

m An A B m Io Bp A B o I

m An A m R

Page 3: Derivation Rules and Justification. The Simple Rules mA nB oA & Bn, m &I mA & B nAn &E oBn &E mA B nA oBm,n E mA B nB oAm,n E pBm,o E mA nA.

Reiteration

m An A m R

, A A

Page 4: Derivation Rules and Justification. The Simple Rules mA nB oA & Bn, m &I mA & B nAn &E oBn &E mA B nA oBm,n E mA B nB oAm,n E pBm,o E mA nA.

Reiteration

, A , A AT T T T TT F T F F

m An A m R

, A A

Page 5: Derivation Rules and Justification. The Simple Rules mA nB oA & Bn, m &I mA & B nAn &E oBn &E mA B nA oBm,n E mA B nB oAm,n E pBm,o E mA nA.

Reiteration

, A , A AT T T T TT F T F F

m An A m R

, A A

Page 6: Derivation Rules and Justification. The Simple Rules mA nB oA & Bn, m &I mA & B nAn &E oBn &E mA B nA oBm,n E mA B nB oAm,n E pBm,o E mA nA.

&Em A & Bn A n &Eo B n &E , A & B A

, A & B B

Page 7: Derivation Rules and Justification. The Simple Rules mA nB oA & Bn, m &I mA & B nAn &E oBn &E mA B nA oBm,n E mA B nB oAm,n E pBm,o E mA nA.

&Em A & Bn A n &Eo B n &E

, A & B A

, A & B B

, A, B , A & B AT T T T T TT T F T F TT F T T F FT F F T F F

, A, B , A & B BT T T T T TT T F T F FT F T T F TT F F T F F

Page 8: Derivation Rules and Justification. The Simple Rules mA nB oA & Bn, m &I mA & B nAn &E oBn &E mA B nA oBm,n E mA B nB oAm,n E pBm,o E mA nA.

&Em A & Bn A n &Eo B n &E

, A & B A

, A & B B

, A, B , A & B AT T T T T TT T F T F TT F T T F FT F F T F F

, A, B , A & B BT T T T T TT T F T F FT F T T F TT F F T F F

Page 9: Derivation Rules and Justification. The Simple Rules mA nB oA & Bn, m &I mA & B nAn &E oBn &E mA B nA oBm,n E mA B nB oAm,n E pBm,o E mA nA.

&Im An Bo A & B n, m &I

, A, B A & B

Page 10: Derivation Rules and Justification. The Simple Rules mA nB oA & Bn, m &I mA & B nAn &E oBn &E mA B nA oBm,n E mA B nB oAm,n E pBm,o E mA nA.

&Im An Bo A & B n, m &I

, A, B A & B

, A, B , A, B A & BT T T T T T TT T F T T F FT F T T F T FT F F T F F F

Page 11: Derivation Rules and Justification. The Simple Rules mA nB oA & Bn, m &I mA & B nAn &E oBn &E mA B nA oBm,n E mA B nB oAm,n E pBm,o E mA nA.

&Im An Bo A & B n, m &I

, A, B A & B

, A, B , A, B A & BT T T T T T TT T F T T F FT F T T F T FT F F T F F F

Page 12: Derivation Rules and Justification. The Simple Rules mA nB oA & Bn, m &I mA & B nAn &E oBn &E mA B nA oBm,n E mA B nB oAm,n E pBm,o E mA nA.

I, A A B

, B A B

m An A B m Io Bp A B o I

Page 13: Derivation Rules and Justification. The Simple Rules mA nB oA & Bn, m &I mA & B nAn &E oBn &E mA B nA oBm,n E mA B nB oAm,n E pBm,o E mA nA.

I, A A B

, B A B

m An A B m Io Bp A B o I

, A, B , A A B T T T T T TT T F T T TT F T T F FT F F T F F

, A, B , B A BT T T T T TT T F T F TT F T T T TT F F T F F

Page 14: Derivation Rules and Justification. The Simple Rules mA nB oA & Bn, m &I mA & B nAn &E oBn &E mA B nA oBm,n E mA B nB oAm,n E pBm,o E mA nA.

I, A A B

, B A B

m An A B m Io Bp A B o I

, A, B , A A B T T T T T TT T F T T TT F T T F FT F F T F F

, A, B , B A BT T T T T TT T F T F TT F T T T TT F F T F F

Page 15: Derivation Rules and Justification. The Simple Rules mA nB oA & Bn, m &I mA & B nAn &E oBn &E mA B nA oBm,n E mA B nB oAm,n E pBm,o E mA nA.

Em A Bn Ao B m,n E

, A B, A B

Page 16: Derivation Rules and Justification. The Simple Rules mA nB oA & Bn, m &I mA & B nAn &E oBn &E mA B nA oBm,n E mA B nB oAm,n E pBm,o E mA nA.

Em A Bn Ao B m,n E

, A B, A B

, A, B , A B, A BT T T T T T TT T F T F T FT F T T T F TT F F T T F F

Page 17: Derivation Rules and Justification. The Simple Rules mA nB oA & Bn, m &I mA & B nAn &E oBn &E mA B nA oBm,n E mA B nB oAm,n E pBm,o E mA nA.

Em A Bn Ao B m,n E

, A B, A B

, A, B , A B, A BT T T T T T TT T F T F T FT F T T T F TT F F T T F F

Page 18: Derivation Rules and Justification. The Simple Rules mA nB oA & Bn, m &I mA & B nAn &E oBn &E mA B nA oBm,n E mA B nB oAm,n E pBm,o E mA nA.

Em A Bn Bo A m,n Ep B m,o E

, A B, A B

, B A, A B

Page 19: Derivation Rules and Justification. The Simple Rules mA nB oA & Bn, m &I mA & B nAn &E oBn &E mA B nA oBm,n E mA B nB oAm,n E pBm,o E mA nA.

Em A Bn Bo A m,n Ep B m,o E

, A B, A B

, B A, A B

, A, B , A B, A BT T T T T T TT T F T F T FT F T T F F TT F F T T F F

, A, B , A B, B AT T T T T T TT T F T F F TT F T T F T FT F F T T F F

Page 20: Derivation Rules and Justification. The Simple Rules mA nB oA & Bn, m &I mA & B nAn &E oBn &E mA B nA oBm,n E mA B nB oAm,n E pBm,o E mA nA.

Em A Bn Bo A m,n Ep B m,o E

, A B, A B

, B A, A B

, A, B , A B, A BT T T T T T TT T F T F T FT F T T F F TT F F T T F F

, A, B , A B, B AT T T T T T TT T F T F F TT F T T F T FT F F T T F F

Page 21: Derivation Rules and Justification. The Simple Rules mA nB oA & Bn, m &I mA & B nAn &E oBn &E mA B nA oBm,n E mA B nB oAm,n E pBm,o E mA nA.

The Complex Rulesm A Assumptionn Bo A B m-n I

m A Assumptionn B

o Bp Aq A B m-n, o-p I

m A B

n A Assumptiono C

p B Assumptionq Cr C m, n-o, p-q I

m A Assumptionn Bo Bp A m-o I

m A Assumptionn Bo Bp A m-o E

Page 22: Derivation Rules and Justification. The Simple Rules mA nB oA & Bn, m &I mA & B nAn &E oBn &E mA B nA oBm,n E mA B nB oAm,n E pBm,o E mA nA.

Im A Assumptionn Bo A B m-n I

If , A B, then A B

Page 23: Derivation Rules and Justification. The Simple Rules mA nB oA & Bn, m &I mA & B nAn &E oBn &E mA B nA oBm,n E mA B nB oAm,n E pBm,o E mA nA.

Im A Assumptionn Bo A B m-n I

If , A B, then A B

, A, B If , A B, then A BT T T T T T T TT T F T T F T FT F T T F T T TT F F T F F T T

Page 24: Derivation Rules and Justification. The Simple Rules mA nB oA & Bn, m &I mA & B nAn &E oBn &E mA B nA oBm,n E mA B nB oAm,n E pBm,o E mA nA.

Im A Assumptionn Bo A B m-n I

If , A B, then A B

, A, B If , A B, then A BT T T T T T T TT T F T T F T FT F T T F T T TT F F T F F T T

Page 25: Derivation Rules and Justification. The Simple Rules mA nB oA & Bn, m &I mA & B nAn &E oBn &E mA B nA oBm,n E mA B nB oAm,n E pBm,o E mA nA.

I

If , A B, and , B A, then A B

m A Assumptionn B

o Bp Aq A B m-n, o-p I

Page 26: Derivation Rules and Justification. The Simple Rules mA nB oA & Bn, m &I mA & B nAn &E oBn &E mA B nA oBm,n E mA B nB oAm,n E pBm,o E mA nA.

I

If , A B, and , B A, then A B

, A, B If , A B, and , B A, then A BT T T T T T T T T T TT T F T T F T F T T FT F T T F T T T F T FT F F T F F T F F T T

m A Assumptionn B

o Bp Aq A B m-n, o-p I

Page 27: Derivation Rules and Justification. The Simple Rules mA nB oA & Bn, m &I mA & B nAn &E oBn &E mA B nA oBm,n E mA B nB oAm,n E pBm,o E mA nA.

I

If , A B, and , B A, then A B

, A, B If , A B, and , B A, then A BT T T T T T T T T T TT T F T T F T F T T FT F T T F T T T F T FT F F T F F T F F T T

m A Assumptionn B

o Bp Aq A B m-n, o-p I

Page 28: Derivation Rules and Justification. The Simple Rules mA nB oA & Bn, m &I mA & B nAn &E oBn &E mA B nA oBm,n E mA B nB oAm,n E pBm,o E mA nA.

Em A B

n A Assumptiono C

p B Assumptionq Cr C m, n-o, p-q I

If , A B, A C, and , A B, B C, then , A B C

Page 29: Derivation Rules and Justification. The Simple Rules mA nB oA & Bn, m &I mA & B nAn &E oBn &E mA B nA oBm,n E mA B nB oAm,n E pBm,o E mA nA.

Em A B

n A Assumptiono C

p B Assumptionq Cr C m, n-o, p-q I

If , A B, A C, and , A B, B C, then , A B C

, A, B, C If , A B, A C, and , A B, B C, then , A B CT T T T T T T T T T T T T T TT T T F T T T F T T T F T T FT T F T T T T T T T F T T T TT T F F T T T F T T F F T T FT F T T T T F T T T T T T T TT F T F T T F F T T T F T T FT F F T T F F T T F F T T F TT F F F T F F F T F F F T F F

Page 30: Derivation Rules and Justification. The Simple Rules mA nB oA & Bn, m &I mA & B nAn &E oBn &E mA B nA oBm,n E mA B nB oAm,n E pBm,o E mA nA.

Em A B

n A Assumptiono C

p B Assumptionq Cr C m, n-o, p-q I

If , A B, A C, and , A B, B C, then , A B C

, A, B, C If , A B, A C, and , A B, B C, then , A B CT T T T T T T T T T T T T T TT T T F T T T F T T T F T T FT T F T T T T T T T F T T T TT T F F T T T F T T F F T T FT F T T T T F T T T T T T T TT F T F T T F F T T T F T T FT F F T T F F T T F F T T F TT F F F T F F F T F F F T F F

Page 31: Derivation Rules and Justification. The Simple Rules mA nB oA & Bn, m &I mA & B nAn &E oBn &E mA B nA oBm,n E mA B nB oAm,n E pBm,o E mA nA.

¬Im A Assumptionn Bo Bp A m-o I

If , A B and , A B, then A

Page 32: Derivation Rules and Justification. The Simple Rules mA nB oA & Bn, m &I mA & B nAn &E oBn &E mA B nA oBm,n E mA B nB oAm,n E pBm,o E mA nA.

¬Im A Assumptionn Bo Bp A m-o I

If , A B and , A B, then A

, A, B If , A B and , A B, then AT T T T T T T T F T FT T F T T F T T T T FT F T T F T T F F T TT F F T F F T F T T T

Page 33: Derivation Rules and Justification. The Simple Rules mA nB oA & Bn, m &I mA & B nAn &E oBn &E mA B nA oBm,n E mA B nB oAm,n E pBm,o E mA nA.

¬Im A Assumptionn Bo Bp A m-o I

If , A B and , A B, then A

, A, B If , A B and , A B, then AT T T T T T T T F T FT T F T T F T T T T FT F T T F T T F F T TT F F T F F T F T T T

Page 34: Derivation Rules and Justification. The Simple Rules mA nB oA & Bn, m &I mA & B nAn &E oBn &E mA B nA oBm,n E mA B nB oAm,n E pBm,o E mA nA.

¬Em A Assumptionn Bo Bp A m-o E

If , A B and , A B, then A

Page 35: Derivation Rules and Justification. The Simple Rules mA nB oA & Bn, m &I mA & B nAn &E oBn &E mA B nA oBm,n E mA B nB oAm,n E pBm,o E mA nA.

¬Em A Assumptionn Bo Bp A m-o E

If , A B and , A B, then A

, A, B If , A B and , A B, then AT T T T T T T T F T FT T F T T F T T T T FT F T T F T T F F T TT F F T F F T F T T T

Page 36: Derivation Rules and Justification. The Simple Rules mA nB oA & Bn, m &I mA & B nAn &E oBn &E mA B nA oBm,n E mA B nB oAm,n E pBm,o E mA nA.

¬Em A Assumptionn Bo Bp A m-o E

If , A B and , A B, then A

, A, B If , A B and , A B, then AT T T T T T T T F T FT T F T T F T T T T FT F T T F T T F F T TT F F T F F T F T T T


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Inclusive e + e - pair production in p+p and p+Nb collisions at E = 3.5 GeV

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