
theorem Th53:
  for I being non empty set
  for J being TopStruct-yielding non-Empty ManySortedSet of I
  for i being Element of I holds (ProjMap J).i = proj(J,i)
proof
  let I be non empty set;
  let J be TopStruct-yielding non-Empty ManySortedSet of I;
  let i be Element of I;
  dom Carrier J = I by PARTFUN1:def 2;
  hence (ProjMap J).i = proj(Carrier J,i) by Def2
    .= proj(J,i) by WAYBEL18:def 4;
end;
