scheme :: CIRCCMB3:sch 18
Comb5CircResult{ F1() -> object , F2() -> object , F3() -> object , F4() -> object , F5() -> object , F6() -> non empty finite set , F7( object , object , object , object , object ) -> Element of F6(), F8() -> finite Signature of F6(), F9() -> Circuit of F6(),F8(), F10() -> Function of (5 -tuples_on F6()),F6() } :
for s being State of (F9() +* (1GateCircuit (<*F1(),F2(),F3(),F4(),F5()*>,F10())))
for s9 being State of F9() st s9 = s | the carrier of F8() holds
for a1, a2, a3, a4, a5 being Element of F6() st ( F1() in InnerVertices F8() implies a1 = (Result s9) . F1() ) & ( not F1() in InnerVertices F8() implies a1 = s . F1() ) & ( F2() in InnerVertices F8() implies a2 = (Result s9) . F2() ) & ( not F2() in InnerVertices F8() implies a2 = s . F2() ) & ( F3() in InnerVertices F8() implies a3 = (Result s9) . F3() ) & ( not F3() in InnerVertices F8() implies a3 = s . F3() ) & ( F4() in InnerVertices F8() implies a4 = (Result s9) . F4() ) & ( not F4() in InnerVertices F8() implies a4 = s . F4() ) & ( F5() in InnerVertices F8() implies a5 = (Result s9) . F5() ) & ( not F5() in InnerVertices F8() implies a5 = s . F5() ) holds
(Result s) . (Output (1GateCircStr (<*F1(),F2(),F3(),F4(),F5()*>,F10()))) = F7(a1,a2,a3,a4,a5)
provided
A1: for g being Function of (5 -tuples_on F6()),F6() holds
( g = F10() iff for a1, a2, a3, a4, a5 being Element of F6() holds g . <*a1,a2,a3,a4,a5*> = F7(a1,a2,a3,a4,a5) ) and
A2: not Output (1GateCircStr (<*F1(),F2(),F3(),F4(),F5()*>,F10())) in InputVertices F8()