reserve a, b, n for Nat,
  r for Real,
  f for FinSequence of REAL;
reserve p for Prime;

theorem Th18:
  for X being set, b1, b2 being real-valued finite-support ManySortedSet of X
  holds support max(b1,b2) c= support b1 \/ support b2
proof
  let X be set;
  let b1, b2 be real-valued finite-support ManySortedSet of X;
  set f = max(b1,b2);
  let x be object;
  assume x in support f;
  then
A1: f.x <> 0 by PRE_POLY:def 7;
  f.x = b1.x or f.x = b2.x by Def4;
  then x in support b1 or x in support b2 by A1,PRE_POLY:def 7;
  hence thesis by XBOOLE_0:def 3;
end;
