
theorem
  for am,bm,cm,dm being non pair set for cin being set st cin <> [<*dm,
GFA3AdderOutput(am,bm,cm)*>,nor2] for s being State of BitFTA3Circ(am,bm,cm,dm
  ,cin) holds Following(s,4) is stable
proof
  set n1=2, n2=2;
  let am,bm,cm,dm be non pair set;
  let cin be set;
  set C = BitFTA3Circ(am,bm,cm,dm,cin);
  set S1 = BitGFA3Str(am,bm,cm);
  set C1 = BitGFA3Circ(am,bm,cm);
  set A1 = GFA3AdderOutput(am,bm,cm);
  set S2 = BitGFA3Str(A1,cin,dm);
  set C2 = BitGFA3Circ(A1,cin,dm);
  set cindm = [<*cin,dm*>,nor2];
  set dmA1 = [<*dm,A1*>, nor2];
  assume
A1: cin <> dmA1;
  let s be State of C;
  C1 tolerates C2 by CIRCCOMB:60;
  then
A2: the Sorts of C1 tolerates the Sorts of C2 by CIRCCOMB:def 3;
  then reconsider s1 = s|the carrier of S1 as State of C1 by CIRCCOMB:26;
  reconsider s2 = Following(s,n1)|the carrier of S2 as State of C2 by A2,
CIRCCOMB:26;
A3: InputVertices S1 misses InnerVertices S2 & Following(s1,n1) is stable by
Lm32,GFACIRC1:136;
  A1<>cindm by Lm31;
  then Following(s2,n2) is stable by A1,GFACIRC1:136;
  then Following(s,n1+n2) is stable by A3,CIRCCMB2:19,CIRCCOMB:60;
  hence thesis;
end;
