
theorem Th49:
  for L being antisymmetric reflexive with_infima RelStr for A, B
  being Subset of L holds A /\ B c= A "/\" B
proof
  let L be antisymmetric reflexive with_infima RelStr, A, B be Subset of L;
  let q be object;
  assume
A1: q in A /\ B;
  then reconsider A1 = A as non empty Subset of L;
  reconsider q1 = q as Element of A1 by A1,XBOOLE_0:def 4;
A2: q1 = q1 "/\" q1 by YELLOW_0:25;
  q in B by A1,XBOOLE_0:def 4;
  hence thesis by A2;
end;
