
theorem Th20:
  for S1,S2,S being non void Circuit-like non empty
ManySortedSign st InputVertices S1 misses InnerVertices S2 & S = S1+*S2 for A1
  being non-empty Circuit of S1, A2 being non-empty Circuit of S2 for A being
non-empty Circuit of S st A1 tolerates A2 & A = A1+*A2 for n1,n2 being Nat st (
for s being State of A1 holds Following(s, n1) is stable) & (for s being State
of A2 holds Following(s, n2) is stable) for s being State of A holds Following(
  s, n1+n2) is stable
proof
  let S1,S2,S be non void Circuit-like non empty ManySortedSign such that
A1: InputVertices S1 misses InnerVertices S2 & S = S1+*S2;
  let A1 be non-empty Circuit of S1, A2 be non-empty Circuit of S2;
  let A be non-empty Circuit of S such that
A2: A1 tolerates A2 and
A3: A = A1+*A2;
  let n1,n2 be Nat such that
A4: ( for s being State of A1 holds Following(s, n1) is stable)& for s
  being State of A2 holds Following(s, n2) is stable;
  let s be State of A;
A5: the Sorts of A1 tolerates the Sorts of A2 by A2,CIRCCOMB:def 3;
  then reconsider s1 = s|the carrier of S1 as State of A1 by A3,CIRCCOMB:26;
  reconsider s2 = Following(s,n1)|the carrier of S2 as State of A2 by A3,A5,
CIRCCOMB:26;
  Following(s1,n1) is stable & Following(s2,n2) is stable by A4;
  hence thesis by A1,A2,A3,Th19;
end;
