
theorem ThSTC0IIS4:
  for x1,x2,x3,x5,x6,x7 being non pair set holds
    InputVertices STC0IIStr(x1,x2,x3,x5,x6,x7) = {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);
    set S1 = BitGFA0Str(x1,x2,x3);
    set S2 = BitGFA0Str(x5,x6,x7);

A1: InputVertices S1 = {x1,x2,x3} & InputVertices S2 = {x5,x6,x7}
    by GFACIRC1:34;
    InnerVertices S1 is Relation & InnerVertices S2 is Relation;
    hence
    InputVertices S
     = {x1,x2,x3} \/ {x5,x6,x7} by A1,FACIRC_1:7
    .= {x1,x2,x3,x5,x6,x7} by ENUMSET1:13;
  end;
