reserve i,j,k,n,m for Nat,
        X for set,
        b,s for bag of X,
        x for object;
reserve O for Ordinal,
        R for right_zeroed add-associative right_complementable
          right_unital distributive non trivial doubleLoopStr,
        p for Polynomial of O, R;
reserve O for Ordinal,
        R for right_zeroed add-associative right_complementable
             right_unital distributive non trivial doubleLoopStr,
        p for Polynomial of O, R;

theorem Th79:
  for X be Ordinal, S be add-associative right_complementable right_zeroed
    right_unital distributive non empty doubleLoopStr
  for p,q be Polynomial of X, S
  for V be set st vars p c= V & vars q c= V holds
    vars (p*'q) c= V
proof
  let X be Ordinal, S be add-associative right_complementable right_zeroed
  right_unital distributive non empty doubleLoopStr;
  let p,q be Polynomial of X, S;
  let V be set;
  assume vars p c= V & vars q c= V;
  then vars (p*'q) c= vars p \/ vars q c= V by Th43,XBOOLE_1:8;
  hence thesis;
end;
