
theorem Th12:
  for x,y,z being set holds InnerVertices GFA0CarryStr(x,y,z) is Relation
proof
  let x,y,z be set;
  set f1 = and2, f2 = and2, f3 = and2, f4 = or3;
  set xy = [<*x,y*>,f1], yz = [<*y,z*>,f2], zx = [<*z,x*>,f3];
  set Cxy = 1GateCircStr(<*x,y*>,f1);
  set Cyz = 1GateCircStr(<*y,z*>,f2);
  set Czx = 1GateCircStr(<*z,x*>,f3);
  set Cxyz = 1GateCircStr(<*xy, yz, zx*>,f4);
  InnerVertices Cxy is Relation & InnerVertices Cyz is Relation by FACIRC_1:38;
  then InnerVertices Czx is Relation & InnerVertices (Cxy +* Cyz) is Relation
  by FACIRC_1:3,38;
  then InnerVertices Cxyz is Relation & InnerVertices GFA0CarryIStr(x,y,z) is
  Relation by FACIRC_1:3,38;
  hence thesis by FACIRC_1:3;
end;
