
theorem ThSTC0IS18:
  for x1,x2,x3,x4,x5,x6,x7 being non pair set
   for s being State of STC0ICirc(x1,x2,x3,x4,x5,x6,x7)
    holds Following(s,4) is stable
  proof
    let x1,x2,x3,x4,x5,x6,x7 be non pair set;
    set C = STC0ICirc(x1,x2,x3,x4,x5,x6,x7);
    set S1 = STC0IIStr(x1,x2,x3,x5,x6,x7);
    set C1 = STC0IICirc(x1,x2,x3,x5,x6,x7);
    set A1out = GFA0AdderOutput(x1,x2,x3);
    set A2out = GFA0AdderOutput(x5,x6,x7);
    set S2 = BitGFA0Str(A1out,A2out,x4);
    set C2 = BitGFA0Circ(A1out,A2out,x4);
    set n1=2, n2=2;

    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 LmSTC0IS2b,ThSTC0IIS12;
    A1out <> [<*A2out,x4*>,and2] & A2out <> [<*x4,A1out*>,and2] by LmSTC0IS1;
    then Following(s2,n2) is stable by GFACIRC1:40;
    then Following(s,n1+n2) is stable by A3,CIRCCMB2:19,CIRCCOMB:60;
    hence thesis;
  end;
