
theorem Th29:
  for S1,S2 being unsplit gate`1=arity gate`2isBoolean non void
  non empty ManySortedSign st InnerVertices S1 misses InputVertices S2 for A1
being Boolean gate`2=den Circuit of S1 for A2 being Boolean gate`2=den Circuit
  of S2 for s being State of A1+*A2, s2 being State of A2 st s2 = s|the carrier
  of S2 holds (Following s)|the carrier of S2 = Following s2
proof
  let S1,S2 be unsplit gate`1=arity gate`2isBoolean non void non empty
  ManySortedSign such that
A1: InnerVertices S1 misses InputVertices S2;
  let A1 be Boolean gate`2=den Circuit of S1;
  let A2 be Boolean gate`2=den Circuit of S2;
  let s be State of A1+*A2, s2 be State of A2 such that
A2: s2 = s|the carrier of S2;
  reconsider s1 = s|the carrier of S1 as State of A1 by Th26;
  dom Following s2 = the carrier of S2 & Following s = (Following s1)+*
  Following s2 by A1,A2,CIRCCOMB:32,60,CIRCUIT1:3;
  hence thesis by FUNCT_4:23;
end;
