
theorem
  for F being finite set, A being FinSequence of bool F, J, K being set
  st J c= K holds union (A, J) c= union (A, K)
proof
  let F be finite set, A be FinSequence of bool F, J, K be set;
  assume
A1: J c= K;
  thus union (A, J) c= union (A, K)
  proof
    let a be object;
    assume a in union (A, J);
    then ex j being set st j in J & j in dom A & a in A.j by Def1;
    hence thesis by A1,Def1;
  end;
end;
