
theorem Th16:
  for x,y,c being set st
  x <> [<*y,c*>, and2] & y <> [<*x,c*>, and2a] & c <> [<*x,y*>, and2a] &
  c <> [<*x,y*>, 'xor'] holds
  InputVertices BitSubtracterWithBorrowStr(x,y,c) = {x,y,c}
proof
  let x,y,c be set such that
A1: x <> [<*y,c*>, and2] and
A2: y <> [<*x,c*>, and2a] and
A3: c <> [<*x,y*>, and2a] and
A4: c <> [<*x,y*>, 'xor'];
A5: InputVertices 2GatesCircStr(x,y,c, 'xor') = {x,y,c} by A4,FACIRC_1:57;
  InputVertices BorrowStr(x,y,c) = {x,y,c} by A1,A2,A3,Th15;
  hence thesis by A5,CIRCCOMB:47,FACIRC_2:21;
end;
