
theorem
  for S1,S2,S being non void Circuit-like non empty ManySortedSign st
  InputVertices S1 misses InnerVertices S2 & InputVertices S2 misses
  InnerVertices S1 & 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 n being Nat, s being State of A for s1 being State of A1 st s1 =
  s|the carrier of S1 for s2 being State of A2 st s2 = s|the carrier of S2 & (
  Following(s1, n) is not stable or Following(s2, n) is not stable) holds
  Following(s, n) is not stable
proof
  let S1,S2,S be non void Circuit-like non empty ManySortedSign such that
A1: InputVertices S1 misses InnerVertices S2 and
A2: InputVertices S2 misses InnerVertices S1 and
A3: 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
A4: A1 tolerates A2 & A = A1+*A2;
  let n be Nat;
  let s be State of A;
  let s0 be State of A1;
  assume s0 = s|the carrier of S1;
  then
A5: Following(s, n)|the carrier of S1 = Following(s0, n) by A1,A3,A4,Th13;
  let s3 be State of A2 such that
A6: s3 = s|the carrier of S2 and
A7: Following(s0, n) is not stable or Following(s3, n) is not stable;
  Following(s, n)|the carrier of S2 = Following(s3, n) by A2,A3,A4,A6,Th14;
  hence thesis by A3,A4,A7,A5,Th17;
end;
