:: CONAFFM semantic presentation
definition
let c
1 be
OrtAfPl;
attr a
1 is
satisfying_DES means :: CONAFFM:def 1
for b
1, b
2, b
3, b
4, b
5, b
6, b
7 being
Element of a
1 holds
( b
1 <> b
2 & b
1 <> b
3 & b
1 <> b
4 & b
1 <> b
5 & b
1 <> b
6 & b
1 <> b
7 & not
LIN b
4,b
5,b
2 & not
LIN b
2,b
3,b
6 &
LIN b
1,b
2,b
3 &
LIN b
1,b
4,b
5 &
LIN b
1,b
6,b
7 & b
2,b
4 // b
3,b
5 & b
2,b
6 // b
3,b
7 implies b
4,b
6 // b
5,b
7 );
attr a
1 is
satisfying_AH means :: CONAFFM:def 2
for b
1, b
2, b
3, b
4, b
5, b
6, b
7 being
Element of a
1 holds
( b
1,b
2 _|_ b
1,b
3 & b
1,b
4 _|_ b
1,b
5 & b
1,b
6 _|_ b
1,b
7 & b
2,b
4 _|_ b
3,b
5 & b
1,b
2 // b
4,b
6 & b
2,b
6 _|_ b
3,b
7 & not b
1,b
6 // b
1,b
2 & not b
1,b
2 // b
1,b
4 implies b
4,b
6 _|_ b
5,b
7 );
attr a
1 is
satisfying_3H means :: CONAFFM:def 3
for b
1, b
2, b
3 being
Element of a
1 holds
not ( not
LIN b
1,b
2,b
3 & ( for b
4 being
Element of a
1 holds
not ( b
4,b
1 _|_ b
2,b
3 & b
4,b
2 _|_ b
1,b
3 & b
4,b
3 _|_ b
1,b
2 ) ) );
attr a
1 is
satisfying_ODES means :
Def4:
:: CONAFFM:def 4
for b
1, b
2, b
3, b
4, b
5, b
6, b
7 being
Element of a
1 holds
( b
1,b
2 _|_ b
1,b
3 & b
1,b
4 _|_ b
1,b
5 & b
1,b
6 _|_ b
1,b
7 & b
2,b
4 _|_ b
3,b
5 & b
2,b
6 _|_ b
3,b
7 & not b
1,b
6 // b
1,b
2 & not b
1,b
2 // b
1,b
4 implies b
4,b
6 _|_ b
5,b
7 );
attr a
1 is
satisfying_LIN means :
Def5:
:: CONAFFM:def 5
for b
1, b
2, b
3, b
4, b
5, b
6, b
7 being
Element of a
1 holds
( b
1 <> b
2 & b
1 <> b
3 & b
1 <> b
4 & b
1 <> b
5 & b
1 <> b
6 & b
1 <> b
7 & b
2 <> b
4 & b
1,b
6 _|_ b
1,b
7 & b
1,b
2 _|_ b
1,b
3 & b
1,b
4 _|_ b
1,b
5 & not
LIN b
1,b
6,b
2 &
LIN b
1,b
2,b
4 &
LIN b
1,b
3,b
5 & b
2,b
6 _|_ b
3,b
7 & b
4,b
6 _|_ b
5,b
7 implies b
2,b
3 // b
4,b
5 );
attr a
1 is
satisfying_LIN1 means :
Def6:
:: CONAFFM:def 6
for b
1, b
2, b
3, b
4, b
5, b
6, b
7 being
Element of a
1 holds
( b
1 <> b
2 & b
1 <> b
3 & b
1 <> b
4 & b
1 <> b
5 & b
1 <> b
6 & b
1 <> b
7 & b
2 <> b
4 & b
1,b
6 _|_ b
1,b
7 & b
1,b
2 _|_ b
1,b
3 & b
1,b
4 _|_ b
1,b
5 & not
LIN b
1,b
6,b
2 &
LIN b
1,b
2,b
4 &
LIN b
1,b
3,b
5 & b
2,b
6 _|_ b
3,b
7 & b
2,b
3 // b
4,b
5 implies b
4,b
6 _|_ b
5,b
7 );
attr a
1 is
satisfying_LIN2 means :: CONAFFM:def 7
for b
1, b
2, b
3, b
4, b
5, b
6, b
7 being
Element of a
1 holds
( b
1 <> b
2 & b
1 <> b
3 & b
1 <> b
4 & b
1 <> b
5 & b
1 <> b
6 & b
1 <> b
7 & b
2 <> b
4 & b
2,b
3 // b
4,b
5 & b
1,b
2 _|_ b
1,b
3 & b
1,b
4 _|_ b
1,b
5 & not
LIN b
1,b
6,b
2 &
LIN b
1,b
2,b
4 &
LIN b
1,b
3,b
5 & b
2,b
6 _|_ b
3,b
7 & b
4,b
6 _|_ b
5,b
7 implies b
1,b
6 _|_ b
1,b
7 );
end;
:: deftheorem Def1 defines satisfying_DES CONAFFM:def 1 :
for b
1 being
OrtAfPl holds
( b
1 is
satisfying_DES iff for b
2, b
3, b
4, b
5, b
6, b
7, b
8 being
Element of b
1 holds
( b
2 <> b
3 & b
2 <> b
4 & b
2 <> b
5 & b
2 <> b
6 & b
2 <> b
7 & b
2 <> b
8 & not
LIN b
5,b
6,b
3 & not
LIN b
3,b
4,b
7 &
LIN b
2,b
3,b
4 &
LIN b
2,b
5,b
6 &
LIN b
2,b
7,b
8 & b
3,b
5 // b
4,b
6 & b
3,b
7 // b
4,b
8 implies b
5,b
7 // b
6,b
8 ) );
:: deftheorem Def2 defines satisfying_AH CONAFFM:def 2 :
for b
1 being
OrtAfPl holds
( b
1 is
satisfying_AH iff for b
2, b
3, b
4, b
5, b
6, b
7, b
8 being
Element of b
1 holds
( b
2,b
3 _|_ b
2,b
4 & b
2,b
5 _|_ b
2,b
6 & b
2,b
7 _|_ b
2,b
8 & b
3,b
5 _|_ b
4,b
6 & b
2,b
3 // b
5,b
7 & b
3,b
7 _|_ b
4,b
8 & not b
2,b
7 // b
2,b
3 & not b
2,b
3 // b
2,b
5 implies b
5,b
7 _|_ b
6,b
8 ) );
:: deftheorem Def3 defines satisfying_3H CONAFFM:def 3 :
for b
1 being
OrtAfPl holds
( b
1 is
satisfying_3H iff for b
2, b
3, b
4 being
Element of b
1 holds
not ( not
LIN b
2,b
3,b
4 & ( for b
5 being
Element of b
1 holds
not ( b
5,b
2 _|_ b
3,b
4 & b
5,b
3 _|_ b
2,b
4 & b
5,b
4 _|_ b
2,b
3 ) ) ) );
:: deftheorem Def4 defines satisfying_ODES CONAFFM:def 4 :
for b
1 being
OrtAfPl holds
( b
1 is
satisfying_ODES iff for b
2, b
3, b
4, b
5, b
6, b
7, b
8 being
Element of b
1 holds
( b
2,b
3 _|_ b
2,b
4 & b
2,b
5 _|_ b
2,b
6 & b
2,b
7 _|_ b
2,b
8 & b
3,b
5 _|_ b
4,b
6 & b
3,b
7 _|_ b
4,b
8 & not b
2,b
7 // b
2,b
3 & not b
2,b
3 // b
2,b
5 implies b
5,b
7 _|_ b
6,b
8 ) );
:: deftheorem Def5 defines satisfying_LIN CONAFFM:def 5 :
for b
1 being
OrtAfPl holds
( b
1 is
satisfying_LIN iff for b
2, b
3, b
4, b
5, b
6, b
7, b
8 being
Element of b
1 holds
( b
2 <> b
3 & b
2 <> b
4 & b
2 <> b
5 & b
2 <> b
6 & b
2 <> b
7 & b
2 <> b
8 & b
3 <> b
5 & b
2,b
7 _|_ b
2,b
8 & b
2,b
3 _|_ b
2,b
4 & b
2,b
5 _|_ b
2,b
6 & not
LIN b
2,b
7,b
3 &
LIN b
2,b
3,b
5 &
LIN b
2,b
4,b
6 & b
3,b
7 _|_ b
4,b
8 & b
5,b
7 _|_ b
6,b
8 implies b
3,b
4 // b
5,b
6 ) );
:: deftheorem Def6 defines satisfying_LIN1 CONAFFM:def 6 :
for b
1 being
OrtAfPl holds
( b
1 is
satisfying_LIN1 iff for b
2, b
3, b
4, b
5, b
6, b
7, b
8 being
Element of b
1 holds
( b
2 <> b
3 & b
2 <> b
4 & b
2 <> b
5 & b
2 <> b
6 & b
2 <> b
7 & b
2 <> b
8 & b
3 <> b
5 & b
2,b
7 _|_ b
2,b
8 & b
2,b
3 _|_ b
2,b
4 & b
2,b
5 _|_ b
2,b
6 & not
LIN b
2,b
7,b
3 &
LIN b
2,b
3,b
5 &
LIN b
2,b
4,b
6 & b
3,b
7 _|_ b
4,b
8 & b
3,b
4 // b
5,b
6 implies b
5,b
7 _|_ b
6,b
8 ) );
:: deftheorem Def7 defines satisfying_LIN2 CONAFFM:def 7 :
for b
1 being
OrtAfPl holds
( b
1 is
satisfying_LIN2 iff for b
2, b
3, b
4, b
5, b
6, b
7, b
8 being
Element of b
1 holds
( b
2 <> b
3 & b
2 <> b
4 & b
2 <> b
5 & b
2 <> b
6 & b
2 <> b
7 & b
2 <> b
8 & b
3 <> b
5 & b
3,b
4 // b
5,b
6 & b
2,b
3 _|_ b
2,b
4 & b
2,b
5 _|_ b
2,b
6 & not
LIN b
2,b
7,b
3 &
LIN b
2,b
3,b
5 &
LIN b
2,b
4,b
6 & b
3,b
7 _|_ b
4,b
8 & b
5,b
7 _|_ b
6,b
8 implies b
2,b
7 _|_ b
2,b
8 ) );
theorem Th1: :: CONAFFM:1
theorem Th2: :: CONAFFM:2
theorem Th3: :: CONAFFM:3
theorem Th4: :: CONAFFM:4
theorem Th5: :: CONAFFM:5
theorem Th6: :: CONAFFM:6