
theorem ThSTC0IIS8:
  for x1,x2,x3,x5,x6,x7 being non pair set holds
    x1 in InputVertices STC0IIStr(x1,x2,x3,x5,x6,x7) &
    x2 in InputVertices STC0IIStr(x1,x2,x3,x5,x6,x7) &
    x3 in InputVertices STC0IIStr(x1,x2,x3,x5,x6,x7) &
    x5 in InputVertices STC0IIStr(x1,x2,x3,x5,x6,x7) &
    x6 in InputVertices STC0IIStr(x1,x2,x3,x5,x6,x7) &
    x7 in InputVertices STC0IIStr(x1,x2,x3,x5,x6,x7)
  proof
    let x1,x2,x3,x5,x6,x7 be non pair set;
    set S = STC0IIStr(x1,x2,x3,x5,x6,x7);

    InputVertices S = {x1,x2,x3,x5,x6,x7} by ThSTC0IIS4;
    hence thesis by ENUMSET1:def 4;
  end;
