reserve x,y,z,c for object,
  f for Function of 2-tuples_on BOOLEAN, BOOLEAN;
reserve s for State of 2GatesCircuit(x,y,c,f);

theorem Th85:
  for x,y,c being non pair object holds InputVertices
  BitAdderWithOverflowStr(x,y,c) = {x,y,c}
proof
  let x,y,c be non pair object;
  set S = BitAdderWithOverflowStr(x,y,c);
  set S1 = 2GatesCircStr(x,y,c, 'xor'), S2 = MajorityStr(x,y,c);
A1: InputVertices S1 = {x,y,c} & InputVertices S2 = {x,y,c} by Th57,Th75;
  InnerVertices S1 is Relation & InnerVertices S2 is Relation by Th58,Th67;
  hence InputVertices S = {x,y,c} \/ {x,y,c} by A1,Th7
    .= {x,y,c};
end;
