
theorem :: ThSTC0S18:
  for x1,x2,x3,x4,x5,x6,x7 being non pair set
   for s being State of STC0Circ(x1,x2,x3,x4,x5,x6,x7)
    holds Following(s,6) is stable
  proof
    let x1,x2,x3,x4,x5,x6,x7 be non pair set;
    set S = STC0Str(x1,x2,x3,x4,x5,x6,x7);
    set C = STC0Circ(x1,x2,x3,x4,x5,x6,x7);
    set S1 = STC0IStr(x1,x2,x3,x4,x5,x6,x7);
    set C1 = STC0ICirc(x1,x2,x3,x4,x5,x6,x7);
    set A1out = GFA0AdderOutput(x1,x2,x3);
    set A2out = GFA0AdderOutput(x5,x6,x7);
    set C1out = GFA0CarryOutput(x1,x2,x3);
    set C2out = GFA0CarryOutput(x5,x6,x7);
    set C3out = GFA0CarryOutput(A1out,A2out,x4);
    set S2 = BitGFA0Str(C1out,C2out,C3out);
    set C2 = BitGFA0Circ(C1out,C2out,C3out);
    set C1C2x = [<*C1out,C2out*>, xor2];
    set C1C2a = [<*C1out,C2out*>, and2];
    set C2C3a = [<*C2out,C3out*>, and2];
    set C3C1a = [<*C3out,C1out*>, and2];
    set n1=4, 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 LmSTC0S2b,ThSTC0IS18;

    C3out <> C1C2x & C1out <> C2C3a & C2out <> C3C1a & C3out <> C1C2a
    by LmSTC0S1;
    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;
