reserve S for 1-sorted,
  i for Element of NAT,
  p for FinSequence,
  X for set;

theorem Th35:
  for X being non empty set, l being Linear_Combination of bspace(
  X), x being Element of bspace(X) st x in Carrier l holds l.x = 1_Z_2
proof
  let X be non empty set, l be Linear_Combination of bspace(X), x be Element
  of bspace(X);
  assume x in Carrier l;
  then l.x <> 0.Z_2 by VECTSP_6:2;
  hence thesis by Th5,Th6,CARD_1:50,TARSKI:def 2;
end;
