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