let S1, S2 be non empty non void unsplit gate`1=arity gate`2isBoolean ManySortedSign ; :: thesis: for A1 being non-empty gate`2=den Boolean Circuit of non-empty gate`2=den Boolean
for A2 being non-empty gate`2=den Boolean Circuit of non-empty gate`2=den Boolean
for s being State of holds
( s | the carrier of S1 is State of & s | the carrier of S2 is State of )
let A1 be gate`2=den Boolean Circuit of gate`2=den Boolean ; :: thesis: for A2 being non-empty gate`2=den Boolean Circuit of non-empty gate`2=den Boolean
for s being State of holds
( s | the carrier of S1 is State of & s | the carrier of S2 is State of )
let A2 be gate`2=den Boolean Circuit of gate`2=den Boolean ; :: thesis: for s being State of holds
( s | the carrier of S1 is State of & s | the carrier of S2 is State of )
let s be State of ; :: thesis: ( s | the carrier of S1 is State of & s | the carrier of S2 is State of )
the Sorts of A1 tolerates the Sorts of A2 by CIRCCOMB:67;
hence ( s | the carrier of S1 is State of & s | the carrier of S2 is State of ) by CIRCCOMB:33; :: thesis: verum