
theorem Th34:
  for x,y,z being non pair set holds InputVertices BitGFA0Str(x,y, z) = {x,y,z}
proof
  let x,y,z be non pair set;
  set S = BitGFA0Str(x,y,z);
  set S1 = GFA0AdderStr(x,y,z);
  set S2 = GFA0CarryStr(x,y,z);
A1: InputVertices S1 = {x,y,z} & InputVertices S2 = {x,y,z} by Th19,FACIRC_1:57
;
  InnerVertices S1 is Relation & InnerVertices S2 is Relation by Th12,
FACIRC_1:58;
  hence InputVertices S = {x,y,z} \/ {x,y,z} by A1,FACIRC_1:7
    .= {x,y,z};
end;
