reserve x,y,c for set;

theorem Th19:
  for x,y,c being non pair set holds InputVertices
  BitSubtracterWithBorrowStr(x,y,c) = {x,y,c}
proof
  let x,y,c be non pair set;
  set S = BitSubtracterWithBorrowStr(x,y,c);
  set S1 = 2GatesCircStr(x,y,c, 'xor'), S2 = BorrowStr(x,y,c);
A1: InputVertices S1 = {x,y,c} & InputVertices S2 = {x,y,c} by Th9,FACIRC_1:57;
  InnerVertices S1 is Relation & InnerVertices S2 is Relation by Th1,
FACIRC_1:58;
  hence InputVertices S = {x,y,c} \/ {x,y,c} by A1,FACIRC_1:7
    .= {x,y,c};
end;
