
theorem ThSTC0IIS12:
  for x1,x2,x3,x5,x6,x7 being non pair set
   for s being State of STC0IICirc(x1,x2,x3,x5,x6,x7)
    holds Following(s,2) is stable
  proof
    let x1,x2,x3,x5,x6,x7 be non pair set;
    set S1 = BitGFA0Str(x1,x2,x3);
    set S2 = BitGFA0Str(x5,x6,x7);
    set C = STC0IICirc(x1,x2,x3,x5,x6,x7);
    set C1 = BitGFA0Circ(x1,x2,x3);
    set C2 = BitGFA0Circ(x5,x6,x7);
    set n1=2, n2=2;

A1: InputVertices S1 misses InnerVertices S2 &
    InputVertices S2 misses InnerVertices S1 by LmSTC0IIS09a;

    let s be State of C;
    reconsider s1 = s|the carrier of S1 as State of C1 by FACIRC_1:26;
    reconsider s2 = s|the carrier of S2 as State of C2 by FACIRC_1:26;
    Following(s1,n1) is stable & Following(s2,n2) is stable by GFACIRC1:40;
    then
    Following(s,max(n1,n2)) is stable by A1,CIRCCOMB:60,CIRCCMB2:22;
    hence thesis;
  end;
