música: sinfoníes: número 1 y número 2. La Trip del Dr.Guery

Sinfonía número 1: [ 12+12 ]

[00+01][00+04][00+04][00+04] = 13k

[00+04][00+07][00+07][00+07] = 25k = 5·5·k

[00+07][00+10][00+10][00+10] = 37k

[00+10][12+01][12+01][12+01] = 49k = 7·7·k

[00+01][00+01][00+04][00+04] = 10k = 2·5·k

[00+04][00+04][00+07][00+07] = 22k = 2·11·k

[00+07][00+07][00+10][00+10] = 34k = 2·17·k

[00+10][00+10][12+01][12+01] = 46k = 2·23·k

Sinfonía número 1: [ 12+12 ]

[00+01][00+02][00+02][00+02] = 07k

[00+04][00+05][00+05][00+05] = 19k

[00+07][00+08][00+08][00+08] = 31k

[00+10][00+11][00+11][00+11] = 43k

[00+01][00+01][00+02][00+02] = 06k = 2·3·1·k

[00+04][00+04][00+05][00+05] = 18k = 2·3·3·k

[00+07][00+07][00+08][00+08] = 30k = 2·3·5·k

[00+10][00+10][00+11][00+11] = 42k = 2·3·7·k

Sinfonía número 2: [ 4+20 <==> 4+(5+4) = 13 ]

[00+01][00+05][00+08][00+05] = 19k

[00+01][00+06][00+10][00+06] = 23k

[00+07][00+11][12+02][00+11] = 43k

[00+07][00+12][12+04][00+12] = 47k

[00+01][00+08][00+01][00+04] = 14k = 2·7·k

[00+01][00+10][00+01][00+06] = 18k = 2·3·3·k

[00+07][12+02][00+07][00+10] = 38k = 2·19·k

[00+07][12+04][00+07][00+12] = 42k = 2·3·7·k

Sinfonía número 2: [ 3+21 <==> 3+(7+3) = 13 ]

[00+01][00+05][00+08][00+05] = 19k

[00+01][00+06][00+09][00+06] = 22k = 2·11·k

[00+07][00+11][12+02][00+11] = 43k

[00+07][00+12][12+03][00+12] = 46k = 2·23·k

[00+01][00+08][00+01][00+04] = 14k = 2·7·k

[00+01][00+09][00+01][00+06] = 17k

[00+07][12+02][00+07][00+10] = 38k = 2·19·k

[00+07][12+03][00+07][00+12] = 41k

La Trip del Dr.Guery:

( ¬p <==> 5q ):

Tot negres + [00+12]:

[00+11][00+04][00+09][00+04][00+07][00+04][00+00][00+04] = 43k

[12+02][00+07][00+12][00+07][00+11][00+07][00+00][00+07] = 65k = 5·23·k

[00+09][00+02][00+07][00+02][00+09][00+02][00+00][00+02] = 33k = 3·11·k

[12+04][00+04][00+12][00+04][00+11][00+04][00+00][00+04] = 55k = 5·11·k

Tot blanques + [12+06]:

[12+05][00+10][12+03][00+10][12+01][00+10][00+00][00+10] = 85k = 5·17·k

[12+08][12+01][12+06][12+01][12+05][12+01][00+00][12+01] = 107k

[12+03][00+08][12+01][00+08][12+03][00+08][00+00][00+08] = 75k = 3·5·5·k

[12+10][00+10][12+06][00+10][12+05][00+10][00+00][00+10] = 97k

[00+11][00+04][00+09][00+04][00+07][00+04][00+09][00+04] = 52k = 4·13·k

[12+02][00+07][00+12][00+07][00+11][00+07][00+12][00+07] = 77k = 7·11·k

[00+09][00+02][00+07][00+02][00+09][00+02][00+07][00+02] = 40k = 8·(5·1)·k

[12+04][00+04][00+12][00+04][00+11][00+04][00+12][00+04] = 67k

[12+05][00+10][12+03][00+10][12+01][00+10][12+03][00+10] = 100k = 4·(5·5)·k

[12+08][12+01][12+06][12+01][12+05][12+01][12+06][12+01] = 125k = (5·5)·(5·1)·k

[12+03][00+08][12+01][00+08][12+03][00+08][12+01][00+08] = 88k = 8·11·k

[12+10][00+10][12+06][00+10][12+05][00+10][12+06][00+10] = 115k = 5·23·k

computació

for( [k] = 1 ; [k] [< n ; [k]++ )

funcions[k](x,y);

for( [k] = not(1) ; [k] [< not(n) ; [k]-- )

funcions[k](x,y);

Mov bx,n

Mov ax,[bx]

Not ax

Not ax

Mov bx, funcions[0]

Inc bx

Xor cx,cx

Inc cx

cicle

Push bx

Push ax

Push cx

Mov si,x

Mov di,[si]

Push di

Mov si,y

Mov di,[si]

Push di

Call [bx]

Pop di

Mov si,y

Mov [si],di

Pop di

Mov si,x

Mov [si],di

Pop cx

Pop ax

Pop bx

Push cx

Xor cx,ax

Jz final

Pop cx

Inc cx

Inc bx

Jmp cicle

final

Mov bx,not(n)

Mov ax,[bx]

Not ax

Mov bx, funcions[not(0)]

Dec bx

Sys cx,cx

Dec cx

cicle

Push bx

Push ax

Push cx

Mov si,x

Mov di,[si]

Push di

Mov si,y

Mov di,[si]

Push di

Call [bx]

Pop di

Mov si,y

Mov [si],di

Pop di

Mov si,x

Mov [si],di

Pop cx

Pop ax

Pop bx

Push cx

Sys cx,ax

Jf final

Pop cx

Dec cx

Dec bx

Jmp cicle

final

funcions[1]( int x, int y )

{

print("%d",[x]+[y]);

[x] = not([x]);

[y] = [y];

}

funcions[2]( int x, int y )

{

print("%d",[x]+[y]);

[x] = [x];

[y] = not([y]);

}

funcions[3]( int x, int y )

{

print("%d",[x]+[y]);

[x] = not([x]);

[y] = [y];

}

funcions[4]( int x, int y )

{

print("%d",[x]+[y]);

[x] = [x];

[y] = not([y]);

}

funcions[not(1)]( int x, int y )

{

print("%d",[x]·[y]);

[x] = not([x]);

[y] = [y];

}

funcions[not(2)]( int x, int y )

{

print("%d",[x]·[y]);

[x] = [x];

[y] = not([y]);

}

funcions[not(3)]( int x, int y )

{

print("%d",[x]·[y]);

[x] = not([x]);

[y] = [y];

}

funcions[not(4)]( int x, int y )

{

print("%d",[x]·[y]);

[x] = [x];

[y] = not([y]);

}

for( [k] = 1 ; [k] [< 4 ; [k]++ )

funcions[k](x,y);

for( [k] = not(1) ; [k] [< not(4) ; [k]-- )

funcions[k](x,y);

funcions[1]( int m, int n , int p , int q )

{

print("%d / %d",( [m]·[q]+[p]·[n] ),( [n]·[q] ));

[m] = not([m]);

[n] = [n];

[p] = [p];

[q] = [q];

}

funcions[2]( int m, int n , int p , int q )

{

print("%d / %d",( [m]·[q]+[p]·[n] ),( [n]·[q] ));

[m] = [m];

[n] = [n];

[p] = not([p]);

[q] = [q];

}

funcions[3]( int m, int n , int p , int q )

{

print("%d / %d",( [m]·[q]+[p]·[n] ),( [n]·[q] ));

[m] = not([m]);

[n] = [n];

[p] = [p];

[q] = [q];

}

funcions[4]( int m, int n , int p , int q )

{

print("%d / %d",( [m]·[q]+[p]·[n] ),( [n]·[q] ));

[m] = [m];

[n] = [n];

[p] = not([p]);

[q] = [q];

}

bombons, valor absolut, psíquica y ecuació de continuitat

Bombó Café exprés-A:

licor destilat [ vapor ] de café amb molta llet.

txocolata amb poca llet.

Bombó Café exprés-B:

licor destilat [ vapor ] de café amb poca llet.

txocolata amb molta llet.

Bombó Planeta:

Nucli de avellana.

Magma de txocolata-A.

Escorça de galeta.

Mar de txocolata-B.

Muntanyes de atmella.

valor absolut:

(-s) < x < s <==> |x| < s

[==>]

Sigui x >] 0 ==>

x < s

(-s) < (-x) [< x < s

|(-s)| > |(-x)| = |x| < s

Sigui x [< (-0) ==>

(-s) < x

(-s) < x [< (-x) < s

|(-s)| > |x| = |(-x)| < s

[<==]

|x| < s

Sigui x >] 0 ==>

(-s) < (-x) [< x [< |x| < s

Sigui x [< 0 ==>

(-s) < x [< (-x) [< |x| < s

Psíquica:

Radiació paranoide física:

corrents elíptics en el cervell-físic.

f(t) = cos(t)+sin(t)

g(t) = cos(t)+(-1)·sin(t)

f(t)·g(t) = cos(2t)

Ecuació de neuro-transmisor-físic forçat:

d_{tt}^{2}[E(t)]+k^{2}·E(t) = anti-div[A(x,y,z)]·c^{2}·cos(2t)

E(t) = anti-div[A(x,y,z)]·c^{2}·( 1/(k^{2}+(-4)) )·cos(2t)

Radiació paranoide psíquica:

corrents hiperbólics en el cervell-psíquic.

f(t) = cosh(t)+i·sinh(t)

g(t) = cosh(t)+(-i)·sinh(t)

f(t)·g(t) = cosh(2t)

Ecuació de neuro-transmisor-psíquic forçat:

d_{tt}^{2}[E(t)]+(ik)^{2}·E(t) = anti-div[A(x,y,z)]·c^{2}·cosh(2t)

E(t) = anti-div[A(x,y,z)]·c^{2}·( 1/((ik)^{2}+4) )·cosh(2t)

corrents elíptics en el cervell-psíquic.

f(t) = cos(t)+i·sin(t)

g(t) = cos(t)+(-i)·sin(t)

f(t)·g(t) = 1

Ecuació de neuro-transmisor-psíquic forçat:

d_{tt}^{2}[E(t)]+(ik)^{2}·E(t) = anti-div[A(x,y,z)]·c^{2}

E(t) = anti-div[A(x,y,z)]·c^{2}·(1/(ik)^{2})

corrents hiperbólics en el cervell-físic.

f(t) = cosh(t)+sinh(t)

g(t) = cosh(t)+(-1)·sinh(t)

f(t)·g(t) = 1

Ecuació de neuro-transmisor-físic forçat:

d_{tt}^{2}[E(t)]+k^{2}·E(t) = anti-div[A(x,y,z)]·c^{2}

E(t) = anti-div[A(x,y,z)]·c^{2}·(1/k^{2})

d_{tt}^{2}[E(t)]+k^{2}·E(t) = anti-div[A(x,y,z)]·c^{2}·( cos(t)+i·sin(t) )

E(t) = anti-div[A(x,y,z)]·c^{2}·( 1/(k^{2}+(-1)) )·( cos(t)+i·sin(t) )

d_{tt}^{2}[E(t)]+k^{2}·E(t) = anti-div[A(x,y,z)]·c^{2}·( cos(t)+(-i)·sin(t) )

E(t) = anti-div[A(x,y,z)]·c^{2}·( 1/(k^{2}+(-1)) )·( cos(t)+(-i)·sin(t) )

Ecuació de continuitat cinemática:

d_{t}[A(t)] = c·div[ A(x,y,z) ]

A_{x}(x,y,z) = a·f(x) = a·f(vt)

A_{y}(x,y,z) = a·f(y) = a·f( (1/2)·gt^{2} )

A_{z}(x,y,z) = a·f(z) = a·f(vt)

A(t) = ac·f(vt)·(1/v)+ac·f( (1/2)·gt^{2} )·(1/gt)+ac·f(vt)·(1/v)

war-game

Salvació:

2 Dadets de 6 cares.

( 4+ & 4+ ) <==> P(4) = (1/2) & P(4) = (1/2)

( 5+ & 3+ ) <==> P(5) = (1/3) & P(3) = (2/3)

( 6 & 2+ ) <==> P(6) = (1/6) & P(2) = (5/6)

Ametralladora:

trets: 5

tipus de dispar: lineal

Lleugera:

salvació: ( 4+ & 4+ )

Pesada:

salvació: ( 5+ & 3+ )

de asalt:

salvació: ( 6 & 2+ )

Llanza-granades:

trets: plantilla de radi: r = 5·cm

tipus de dispar: parabólic

Lleugera:

salvació: ( 4+ & 4+ )

Pesada:

salvació: ( 5+ & 3+ )

de asalt:

salvació: ( 6 & 2+ )

Ametralladora láser:

trets: 10

tipus de dispar: lineal

Lleugera:

salvació: ( 4+ & 4+ )

Pesada:

salvació: ( 5+ & 3+ )

de asalt:

salvació: ( 6 & 2+ )

Llanza-granades de plasma-fusió:

trets: plantilla de radi: r = 10·cm

tipus de dispar: parabólic

Lleugera:

salvació: ( 4+ & 4+ )

Pesada:

salvació: ( 5+ & 3+ )

de asalt:

salvació: ( 6 & 2+ )

màxims y mínims, dualogía

teorema:

max{n: f(n) = n+p } = max{n: f(n) = n }+p

min{n: f(n) = n+p } = min{n: f(n) = n }+p

teorema:

sup{n: f(n) = n+p } = sup{n: f(n) = n }+p

inf{n: f(n) = n+p } = inf{n: f(n) = n }+p

demostració per absurd:

max{n: f(n) = n+p } != max{n: f(n) = n }+p

n [< max{n: f(n) = n }

n+p [< max{n: f(n) = n }+p = a < max{n: f(n) = n+p }

n+p [< a < max{n: f(n) = n+p }

n+p [< max{n: f(n) = n+p } = b+p < max{n: f(n) = n }+p

n [< b < max{n: f(n) = n }

Dualogía paralela a una funció:

f(x+cos(s)·h)+f(x+(-1)·cos(s)·h) = F(x)

g(a)+y(a) = 0

( x+cos(s)·h )+( x+(-1)·cos(s)·h ) = 2x

g(0) = (cos(s)·h)

y(0) = (-1)·(cos(s)·h)

( x+cos(s)·h )^{2}+( x+(-1)·cos(s)·h )^{2} = 2·(x+i·cos(s)·h)·(x+(-i)·cos(s)·h)

g(i·cos(s)·h) = 2i·(cos(s)·h)

y(i·cos(s)·h) = (-2)·i·(cos(s)·h)

( x+cos(s)·h )^{3}+( x+(-1)·cos(s)·h )^{3} = 2·x·(x^{2}+3(cos(s)·h))

g(i·3^{(1/2)}·(cos(s)·h)^{(1/2)}) = (-8)·(cos(s)·h)^{3}

y(i·3^{(1/2)}·(cos(s)·h)^{(1/2)}) = 8·(cos(s)·h)^{3}

( x+cos(s)·h )^{4}+( x+(-1)·cos(s)·h )^{4} = ...

... 2·( ( x^{2}+(cos(s)·h)^{2} )^{2}+4x^{2}·(cos(s)h)^{2} )

x^{2}+2i·x·(cos(s)·h)+(cos(s)·h)^{2} = 0

x = ((-1)+2^{(1/2)})·i·(cos(s)·h)

( (-1)+2^{(1/2)} )^{4}·i^{4} = 1+(-4)·2^{(1/2)}+6·2+(-4)·2^{(3/2)}+4

6·( (-1)+2^{(1/2)} )^{2}·i^{2} = 6·( (-1)+2·2^{(1/2)}+(-2) )

g( ((-1)+2^{(1/2)})·i·(cos(s)·h) ) = ...

... ((-1)+2^{(1/2)})·i·(cos(s)·h)^{4}+(-1)·((-1)+2^{(1/2)})^{3}·i·(cos(s)·h)^{4}

y( ((-1)+2^{(1/2)})·i·(cos(s)·h) ) = ...

... (-1)·((-1)+2^{(1/2)})·i·(cos(s)·h)^{4}+((-1)+2^{(1/2)})^{3}·i·(cos(s)·h)^{4}

En símbol de polinómic potencial:

( x+cos(s)·h )^{7}+( x+(-1)·cos(s)·h )^{7} = ...

... 2·x·( x^{6}+21x^{4}(cos(s)·h)^{2}+35x^{2}(cos(s)·h)^{4}+7·(cos(s)·h)^{6} )

(-7)·( cos(s)·h )^{6} = ...

x^{4+[...( 21·(cos(s)·h)^{2} )...[2]...( 21·(cos(s)·h)^{2} )...]}+35x^{2}(cos(s)·h)^{4} = ...

x^{2+[...( 35·(cos(s)·h)^{4} )...[...

... 2+[...( 21·(cos(s)·h)^{2} )...[2]...( 21·(cos(s)·h)^{2} )...]...

... ]...( 35·(cos(s)h)^{4} )...]}

x = ( (-7)·(cos(s)·h)^{6} )^{( 1/( 2+[...( 35·(cos(s)·h)^{4} )...[...

... 2+[...( 21·(cos(s)·h)^{2} )...[2]...( 21·(cos(s)·h)^{2} )...]...

... ]...( 35·(cos(s)h)^{4} )...] ) )}

x^{7}+21x^{5}(cos(s)·h)^{2} = ...

... ( (-7)·(cos(s)·h)^{6} )^{( ...

... ( 5+[...( 21·(cos(s)·h)^{2} )...[2]...( 21·(cos(s)·h)^{2} )...] )/...

... ( 2+[...( 35·(cos(s)·h)^{4} )...[...

... 2+[...( 21·(cos(s)·h)^{2} )...[2]...( 21·(cos(s)·h)^{2} )...]...

... ]...( 35·(cos(s)h)^{4} )...] ) )}

x^{7}+21x^{5}(cos(s)·h)^{2}+35x^{3}(cos(s)·h)^{4} = ...

... ( (-7)·(cos(s)·h)^{6} )^{( ...

... ( 3+[...( 35·(cos(s)·h)^{4} )...[...

... 2+[...( 21·(cos(s)·h)^{2} )...[2]...( 21·(cos(s)·h)^{2} )...]...

...]...( 35·(cos(s)·h)^{4} )...] )/...

... ( 2+[...( 35·(cos(s)·h)^{4} )...[...

... 2+[...( 21·(cos(s)·h)^{2} )...[2]...( 21·(cos(s)·h)^{2} )...]...

... ]...( 35·(cos(s)h)^{4} )...] ) )} = ...

x^{7}+21x^{5}(cos(s)·h)^{2}+35x^{3}(cos(s)·h)^{4} = ...

... (-7)·(cos(s)·h)^{6}·( (-7)·(cos(s)·h)^{6} )^{( 1/( 2+[...( 35·(cos(s)·h)^{4} )...[...

... 2+[...( 21·(cos(s)·h)^{2} )...[2]...( 21·(cos(s)·h)^{2} )...]...

... ]...( 35·(cos(s)h)^{4} )...] ) )}

françé

Françé:

ye parle ye-de-muá

tú parle tú-de-tuá

parle pont-de-suá

nus parloms

vus parloz

parlen pont-de-suá

Françé de le Patuá:

ye parlû-puá

tú parles-puá

parle-puá

nus parlems-de-puá

vus parlez-de-puá

parlen-puá

Françé:

ye vatxne ye-de-muá

tú vatxne tú-de-tuá

vatxne pont-de-suá

nus vatxnoms

vus vatxnoz

vatxnen pont-de-suá

Françé de le Patuá:

ye vaitx-de-puá

tú vas-de-puá

va-de-puá

nus vatxnems-de-puá

vus vatxnez-de-puá

vatxnen-puá

Françé:

ye pode ye-de-muá

tú pode tú-de-tuá

pode pont-de-suá

nus podoms

vus podoz

poden pont-de-suá

Françé de le Patuá:

ye puc-de-puá

tú pots-de-puá

pot-de-puá

nus podems-de-puá

vus podez-de-puá

poden-puá

Françé:

ye vule ye-de-muá

tú vule tú-de-tuá

vule pont-de-suá

nus vuloms

vus vuloz

vulen pont-de-suá

Françé de le Patuá:

ye vull-de-puá

tú vols-de-puá

vol-de-puá

nus vulems-de-puá

vus vulez-de-puá

vulen-puá

limits

x^{n+1}+(-1) = (x+(-1))·(1+x+...(n)...+x^{n})

A(x) = ( (x^{(n+1)}+(-1))/(x+(-1)) )

A(1) = (n+1)

E(x) = ( ((n+1)·x^{n})/(x+(-1)) )+(-1)·( (x^{(n+1)}+(-1))/(x+(-1))^{2} )

E(1) = 0

A(x) = ( (x^{n+1}+(-1))/(x^{m}+(-1)) )

A(1) = ( (n+1)/m )

E(x) = ( ((n+1)·x^{n})/(x^{m}+(-1)) )+...

... (-1)·( (x^{(n+1)}+(-1))/(x^{m}+(-1))^{2} )·mx^{m+(-1)}

E(1) = 0

Tecnología industrial:

PV

kT

qA

qRI

hf

qgx

(1/2)·ax^{2}

(4/3)·Px^{3}

Px^{2}y

(2s)·x^{4}

s·x^{2}yz

(-1)·ln(1+(-x)) = x+...(n)...+(1/n)·x^{n}+...

(-1)·ln(1+x) = (-x)+...(n)...+(-1)^{n}·(1/n)·x^{n}+...

para-constructores, Lagrange y lógica matemàtica

azúcares de nitrógeno:

-C=C=C-O-C=C=C-(NH)-

1 para-constructor

-C=C-O-C=C-(NH)-

1 para-destructor

-C=C=C-O-C=C=C-N-O-O-N-C=C=C-O-C=C=C-

2 para-constructores

-C=C-O-C=C-N-O-O-N-C=C-O-C=C-

2 para-destructores

Azúcares de octo-metal-5:

-C=C=C-O-C=C=C-(PH_{3})-

1 para-constructor

-C=C-O-C=C-(PH_{3})-

1 para-destructor

-C=C=C-O-C=C=C-(PH_{2})-O-O-(PH_{2})-C=C=C-O-C=C=C-

2 para-constructores

-C=C-O-C=C-(PH_{2})-O-O-(PH_{2})-C=C-O-C=C-

2 para-destructores

Azúcares de octo-metal-7:

-C=C=C-O-C=C=C-(SH_{5})-

1 para-constructor

-C=C-O-C=C-(SH_{5})-

1 para-destructor

-C=C=C-O-C=C=C-(SH_{4})-O-O-(SH_{4})-C=C=C-O-C=C=C-

2 para-constructores

-C=C-O-C=C-(SH_{4})-O-O-(SH_{4})-C=C-O-C=C-

2 para-destructores

Amar la vida en este mundo,

supera al no matarás.

Odiar la vida en este mundo,

supera al matarás.

Amar más al que no es que al que es,

supera al no matarás al que es.

Odiar más al que no es que al que es,

supera al matarás al que es. [ La clausula ]

F(x,y,z) = 2·( z+(-1)·(1/2)·z^{2} )+xy+(-h)·( px+qy+(-m) )

d_{x}[F(x,y,z)] = y+(-h)p

d_{y}[F(x,y,z)] = x+(-h)q

2yx = hm

x = 1 & y = 1 & z = 1

h = (2/m)

F(1,1,1) = 2

G(x,y,z) = 2·( z+(-1)·(1/2)·z^{2} )+xy+(-h)·( px+qy )

G(1,1,1) = 0

F(x,y,z) = (2n+(-4))·( z+(-1)·(1/2)·z^{2} )+x^{n+(-k)}+y^{k}+(-h)·( px+qy+(-m) )

d_{x}[F(x,y,z)] = (n+(-k))·x^{n+(-k)+(-1)}+(-h)p

d_{y}[F(x,y,z)] = ky^{k+(-1)}+(-h)q

(n+(-k))·x^{n+(-k)}+ky^{k} = hm

x = 1 & y = 1 & z = 1

h = (n/m)

F(1,1,1) = n

G(x,y,z) = (2n+(-4))·( z+(-1)·(1/2)·z^{2} )+x^{n+(-k)}+y^{k}+(-h)·( px+qy )

G(1,1,1) = 0

F(x,y,z) = (n+(-2))·( e^{z}+(-z) )+e^{(n+(-k))·x}+e^{k·y}+(-h)·( pe^{x}+qe^{y}+(-m) )

d_{x}[F(x,y,z)] = (n+(-k))·e^{(n+(-k))·x}+(-h)pe^{x}

d_{y}[F(x,y,z)] = ke^{k·y}+(-h)qe^{y}

(n+(-k))·e^{(n+(-k))·x}+ke^{k·y} = hm

x = 0 & y = 0 & z = 0

h = (n/m)

F(0,0,0) = n

G(x,y,z) = (n+(-2))·( e^{z}+(-z) )+e^{(n+(-k))·x}+e^{k·y}+(-h)·( pe^{x}+qe^{y} )

G(0,0,0) = 0

[f_{k}] |= [g_{k}] <==> [Av][ v( f_{k} ==> g_{k} ) = 1 ]

[f_{k}] =| [g_{k}] <==> [Av][ v( f_{k} <== g_{k} ) = 1 ]

[f_{k}] |=| [g_{k}] <==> [Av][ v( f_{k} <==> g_{k} ) = 1 ]

[f_{i},f_{j}] |=| [f_{j},f_{i}]

[¬f_{i},¬f_{j}] |=| [¬f_{j},¬f_{i}]

[Av][ v( ( f_{i} & f_{j} ) <==> ( f_{j} & f_{i} ) ) = 1 ]

[Av][ v( ( ¬f_{i} & ¬f_{j} ) <==> ( ¬f_{j} & ¬f_{i} ) ) = 1 ]

]f_{i},f_{j}[ |=| ]f_{j},f_{i}[

]¬f_{i},¬f_{j}[ |=| ]¬f_{j},¬f_{i}[

[Av][ v( ( ¬f_{i} || ¬f_{j} ) <==> ( ¬f_{j} || ¬f_{i} ) ) = 1 ]

[Av][ v( ( f_{i} || f_{j} ) <==> ( f_{j} || f_{i} ) ) = 1 ]

[f_{k},f_{k}] |=| [f_{k}]

]f_{k},f_{k}[ |=| ]f_{k}[

[f_{k}] |=| ]¬f_{k}[

]f_{k}[ |=| [¬f_{k}]

[f_{k},(f_{k} ==> g_{k})] |= [g_{k}] <==> ...

... [Av][ v( ( f_{k} & (f_{k} ==> g_{k}) ) ==> g_{k} ) = 1 ]

[f_{k}] =| [(f_{k} <== g_{k}),g_{k}] <==> ...

... [Av][ v( f_{k} <== ( (f_{k} <== g_{k}) & g_{k} ) ) = 1 ]

Si [Ef_{n}][ f_{0} & [f_{n+(-1)}] |= [f_{n}] ] ==> [f_{0}] |= [f_{n}]

Es defineish:

[f_{n}] |= [f_{n+1}]

[Av][ v( ( f_{0} ==> f_{n} ) & ( f_{n} ==> f_{n+1} ) ) ==> ( f_{0} ==> f_{n+1} ) ) = 1 ]

[Av][ v( f_{0} ==> f_{n+1} ) = 1 ]

Si [Ef_{n}][ f_{0} & [f_{n+(-1)}] |=| [f_{n}] ] ==> [f_{0}] |=| [f_{n}]

Es defineish:

[f_{n}] |=| [f_{n+1}]

[Av][ v( ( f_{0} <==> f_{n} ) & ( f_{n} <==> f_{n+1} ) ) ==> ...

... ( f_{0} <==> f_{n+1} ) ) = 1 ]

[Av][ v( f_{0} <==> f_{n+(-1)} ) = 1 ]

Si f_{k} [€] E ==> E |= [f_{k}]

E = [f_{k},g_{1},...(n)...,g_{n}]

[Av][ v( ( f_{k} & g_{1} & ...(n)... & g_{n} ) ==> f_{k} ) = 1 ]

Si ¬f_{k} [€] ¬E ==> ¬E =| [¬f_{k}]

¬E = ]f_{k},g_{1},...(n)...,g_{n}[

[Av][ v( ¬f_{k} ==> ( ¬f_{k} || ¬g_{1} || ...(n)... || ¬g_{n} ) ) = 1 ]

Si [f_{k}] |= [f_{k+1}] & [g_{k}] |= [g_{k+1}] ==> [f_{k},g_{k}] |= [f_{k+1},g_{k+1}]

Si ]f_{k+1}[ |= ]f_{k}[ & ]g_{k+1}[ |= ]g_{k}[ ==> ]f_{k+1},g_{k+1}[ |= ]f_{k},g_{k}[

[f_{k},g_{k}] |= ...

... [f_{k},(f_{k} ==> f_{k+1}),g_{k},(g_{k} ==> g_{k+1})] |= ...

... [f_{k+1},g_{k+1}]

[Av][ v( ( f_{k} & f_{k} |= f_{k+1} ) <==> f_{k} ) = 1 ]

Si [f_{0}] =| [f_{k}] & [f_{1},...(n)...,f_{n}] =| [f_{0}] ==> [f_{k}] |=| [f_{0}]

Si ]f_{0}[ |= ]f_{k}[ & ]f_{1},...(n)...,f_{n}[ |= ]f_{0}[ ==> ]f_{k}[ |=| ]f_{0}[