
theorem
  for ap,bp,cp,dp being non pair set for cin being set st cin <> [<*dp,
GFA0AdderOutput(ap,bp,cp)*>,and2] for s being State of BitFTA0Circ(ap,bp,cp,dp,
  cin) holds Following(s,4) is stable
proof
  set n1=2, n2=2;
  let ap,bp,cp,dp be non pair set;
  let cin be set;
  set C = BitFTA0Circ(ap,bp,cp,dp,cin);
  set S1 = BitGFA0Str(ap,bp,cp);
  set C1 = BitGFA0Circ(ap,bp,cp);
  set A1 = GFA0AdderOutput(ap,bp,cp);
  set S2 = BitGFA0Str(A1,cin,dp);
  set C2 = BitGFA0Circ(A1,cin,dp);
  set cindp = [<*cin,dp*>,and2];
  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
Lm2,GFACIRC1:40;
  A1<>cindp by Lm1;
  then Following(s2,n2) is stable by A1,GFACIRC1:40;
  then Following(s,n1+n2) is stable by A3,CIRCCMB2:19,CIRCCOMB:60;
  hence thesis;
end;
