let x, y, c be object ; :: thesis: for f being Function of (2 -tuples_on BOOLEAN),BOOLEAN holds
( x in the carrier of (2GatesCircStr (x,y,c,f)) & y in the carrier of (2GatesCircStr (x,y,c,f)) & c in the carrier of (2GatesCircStr (x,y,c,f)) )
let f be Function of (2 -tuples_on BOOLEAN),BOOLEAN; :: thesis: ( x in the carrier of (2GatesCircStr (x,y,c,f)) & y in the carrier of (2GatesCircStr (x,y,c,f)) & c in the carrier of (2GatesCircStr (x,y,c,f)) )
set S1 = 1GateCircStr (<*x,y*>,f);
set S2 = 1GateCircStr (<*[<*x,y*>,f],c*>,f);
A1: c in the carrier of (1GateCircStr (<*[<*x,y*>,f],c*>,f)) by Th43;
( x in the carrier of (1GateCircStr (<*x,y*>,f)) & y in the carrier of (1GateCircStr (<*x,y*>,f)) ) by Th43;
hence ( x in the carrier of (2GatesCircStr (x,y,c,f)) & y in the carrier of (2GatesCircStr (x,y,c,f)) & c in the carrier of (2GatesCircStr (x,y,c,f)) ) by A1, Th20; :: thesis: verum