reserve a,b,c for set;
reserve r for Real,
  X for set,
  n for Element of NAT;

theorem Th42:
  for X being non empty set, X0 being set for A being proper
  Subset of X0-DiscreteTop(X) holds Int A = A /\ X0
proof
  let X be non empty set, X0 be set;
  let A be proper Subset of X0-DiscreteTop(X);
  the carrier of X0-DiscreteTop X = X by Def8;
  then
A1: X <> A by SUBSET_1:def 6;
  thus Int A = IFEQ(A,X,A,A /\ X0) by Def8
    .= A /\ X0 by A1,FUNCOP_1:def 8;
end;
