:: MSSCYC_2 semantic presentation
definition
let c
1 be
ManySortedSign ;
defpred S
1[
set ] means ex b
1, b
2 being
set st
( a
1 = [b1,b2] & b
1 in the
OperSymbols of c
1 & b
2 in the
carrier of c
1 & ex b
3 being
Natex b
4 being
Element of the
carrier of c
1 * st
( the
Arity of c
1 . b
1 = b
4 & b
3 in dom b
4 & b
4 . b
3 = b
2 ) );
func InducedEdges c
1 -> set means :
Def1:
:: MSSCYC_2:def 1
for b
1 being
set holds
( b
1 in a
2 iff ex b
2, b
3 being
set st
( b
1 = [b2,b3] & b
2 in the
OperSymbols of a
1 & b
3 in the
carrier of a
1 & ex b
4 being
Natex b
5 being
Element of the
carrier of a
1 * st
( the
Arity of a
1 . b
2 = b
5 & b
4 in dom b
5 & b
5 . b
4 = b
3 ) ) );
existence
ex b1 being set st
for b2 being set holds
( b2 in b1 iff ex b3, b4 being set st
( b2 = [b3,b4] & b3 in the OperSymbols of c1 & b4 in the carrier of c1 & ex b5 being Natex b6 being Element of the carrier of c1 * st
( the Arity of c1 . b3 = b6 & b5 in dom b6 & b6 . b5 = b4 ) ) )
uniqueness
for b1, b2 being set holds
( ( for b3 being set holds
( b3 in b1 iff ex b4, b5 being set st
( b3 = [b4,b5] & b4 in the OperSymbols of c1 & b5 in the carrier of c1 & ex b6 being Natex b7 being Element of the carrier of c1 * st
( the Arity of c1 . b4 = b7 & b6 in dom b7 & b7 . b6 = b5 ) ) ) ) & ( for b3 being set holds
( b3 in b2 iff ex b4, b5 being set st
( b3 = [b4,b5] & b4 in the OperSymbols of c1 & b5 in the carrier of c1 & ex b6 being Natex b7 being Element of the carrier of c1 * st
( the Arity of c1 . b4 = b7 & b6 in dom b7 & b7 . b6 = b5 ) ) ) ) implies b1 = b2 )
end;
:: deftheorem Def1 defines InducedEdges MSSCYC_2:def 1 :
theorem Th1: :: MSSCYC_2:1
:: deftheorem Def2 defines InducedSource MSSCYC_2:def 2 :
:: deftheorem Def3 defines InducedTarget MSSCYC_2:def 3 :
:: deftheorem Def4 defines InducedGraph MSSCYC_2:def 4 :
theorem Th2: :: MSSCYC_2:2
theorem Th3: :: MSSCYC_2:3
theorem Th4: :: MSSCYC_2:4
theorem Th5: :: MSSCYC_2:5
theorem Th6: :: MSSCYC_2:6