
theorem Th9:
  for S1,S2 being non void Circuit-like non empty ManySortedSign
st InputVertices S1 misses InnerVertices S2 for S being non void Circuit-like
  non empty ManySortedSign st S=S1 +* S2 for A1 being non-empty Circuit of S1
  for A2 being non-empty Circuit of S2 st A1 tolerates A2 for A being non-empty
Circuit of S st A = A1 +* A2 for s being State of A for s1 being State of A1 st
  s1 = s|the carrier of S1 & s1 is stabilizing for s2 being State of A2 st s2 =
Following(s, stabilization-time s1)|the carrier of S2 & s2 is stabilizing holds
  s is stabilizing
proof
  let S1,S2 be non void Circuit-like non empty ManySortedSign such that
A1: InputVertices S1 misses InnerVertices S2;
  let S be non void Circuit-like non empty ManySortedSign such that
A2: S = S1 +* S2;
  let A1 be non-empty Circuit of S1;
  let A2 be non-empty Circuit of S2;
  assume
A3: A1 tolerates A2;
  let A be non-empty Circuit of S such that
A4: A = A1 +* A2;
  let s be State of A;
  let s1 be State of A1 such that
A5: s1 = s|the carrier of S1 and
A6: s1 is stabilizing;
  set n1 = stabilization-time s1;
A7: Following(s1,n1) is stable by A6,Def5;
  let s2 be State of A2 such that
A8: s2 = Following(s, n1)|the carrier of S2 and
A9: s2 is stabilizing;
  set n2 = stabilization-time s2;
  Following(s2,n2) is stable by A9,Def5;
  then Following(s,n1+n2) is stable by A1,A2,A3,A4,A5,A7,A8,CIRCCMB2:19;
  hence thesis;
end;
