
theorem
  for am,bp,cm,dp being non pair set for cin being set st cin <> [<*dp,
GFA2AdderOutput(am,bp,cm)*>,and2] for s being State of BitFTA2Circ(am,bp,cm,dp,
  cin) holds Following(s,4) is stable
proof
  set n1=2, n2=2;
  let am,bp,cm,dp be non pair set;
  let cin be set;
  set C = BitFTA2Circ(am,bp,cm,dp,cin);
  set S1 = BitGFA2Str(am,bp,cm);
  set C1 = BitGFA2Circ(am,bp,cm);
  set A1 = GFA2AdderOutput(am,bp,cm);
  set S2 = BitGFA1Str(A1,cin,dp);
  set C2 = BitGFA1Circ(A1,cin,dp);
  set dpA1 = [<*dp,A1*>, and2 ];
  assume
A1: cin <> dpA1;
  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
Lm22,GFACIRC1:104;
  Following(s2,n2) is stable by A1,Lm21,GFACIRC1:72;
  then Following(s,n1+n2) is stable by A3,CIRCCMB2:19,CIRCCOMB:60;
  hence thesis;
end;
