reserve i,k for Nat;
reserve A for QC-alphabet;
reserve x for bound_QC-variable of A;
reserve a for free_QC-variable of A;
reserve p,q for Element of QC-WFF(A);
reserve l for FinSequence of QC-variables(A);
reserve P,Q for QC-pred_symbol of A;
reserve V for non empty Subset of QC-variables(A);
reserve s,t for QC-symbol of A;

theorem
  Free(p <=> q) = Free p \/ Free q
proof
  p <=> q = (p => q) '&' (q => p) by QC_LANG2:def 4;
  hence Free(p <=> q) = Free (p => q) \/ Free (q => p) by Th42
    .= Free p \/ Free q \/ Free (q => p) by Th60
    .= Free p \/ Free q \/ (Free p \/ Free q) by Th60
    .= Free p \/ Free q;
end;
