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 S1

for A2 being non-empty gate`2=den Boolean Circuit of S2

for s being State of (A1 +* A2) holds

( s | the carrier of S1 is State of A1 & s | the carrier of S2 is State of A2 )

let A1 be gate`2=den Boolean Circuit of S1; :: thesis: for A2 being non-empty gate`2=den Boolean Circuit of S2

for s being State of (A1 +* A2) holds

( s | the carrier of S1 is State of A1 & s | the carrier of S2 is State of A2 )

let A2 be gate`2=den Boolean Circuit of S2; :: thesis: for s being State of (A1 +* A2) holds

( s | the carrier of S1 is State of A1 & s | the carrier of S2 is State of A2 )

let s be State of (A1 +* A2); :: thesis: ( s | the carrier of S1 is State of A1 & s | the carrier of S2 is State of A2 )

the Sorts of A1 tolerates the Sorts of A2 by CIRCCOMB:59;

hence ( s | the carrier of S1 is State of A1 & s | the carrier of S2 is State of A2 ) by CIRCCOMB:26; :: thesis: verum

for A2 being non-empty gate`2=den Boolean Circuit of S2

for s being State of (A1 +* A2) holds

( s | the carrier of S1 is State of A1 & s | the carrier of S2 is State of A2 )

let A1 be gate`2=den Boolean Circuit of S1; :: thesis: for A2 being non-empty gate`2=den Boolean Circuit of S2

for s being State of (A1 +* A2) holds

( s | the carrier of S1 is State of A1 & s | the carrier of S2 is State of A2 )

let A2 be gate`2=den Boolean Circuit of S2; :: thesis: for s being State of (A1 +* A2) holds

( s | the carrier of S1 is State of A1 & s | the carrier of S2 is State of A2 )

let s be State of (A1 +* A2); :: thesis: ( s | the carrier of S1 is State of A1 & s | the carrier of S2 is State of A2 )

the Sorts of A1 tolerates the Sorts of A2 by CIRCCOMB:59;

hence ( s | the carrier of S1 is State of A1 & s | the carrier of S2 is State of A2 ) by CIRCCOMB:26; :: thesis: verum