
theorem Th28:
  for S1,S2 being unsplit gate`1=arity gate`2isBoolean non void
  non empty ManySortedSign st InnerVertices S2 misses InputVertices S1 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, s1 being State of A1 st s1 = s|the carrier
  of S1 holds (Following s)|the carrier of S1 = Following s1
proof
  let S1,S2 be unsplit gate`1=arity gate`2isBoolean non void non empty
  ManySortedSign such that
A1: InnerVertices S2 misses InputVertices S1;
  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, s1 be State of A1 such that
A2: s1 = s|the carrier of S1;
  reconsider s2 = s|the carrier of S2 as State of A2 by Th26;
  dom Following s1 = the carrier of S1 & Following s = (Following s2)+*
  Following s1 by A1,A2,CIRCCOMB:33,60,CIRCUIT1:3;
  hence thesis by FUNCT_4:23;
end;
