consider f being set , p being FinSequence;
take
1GateCircStr (p,f)
; ( 1GateCircStr (p,f) is unsplit & 1GateCircStr (p,f) is gate`1=arity & not 1GateCircStr (p,f) is void & 1GateCircStr (p,f) is strict & not 1GateCircStr (p,f) is empty )
thus
( 1GateCircStr (p,f) is unsplit & 1GateCircStr (p,f) is gate`1=arity & not 1GateCircStr (p,f) is void & 1GateCircStr (p,f) is strict & not 1GateCircStr (p,f) is empty )
; verum