reserve A for QC-alphabet;
reserve sq for FinSequence,
  x,y,z for bound_QC-variable of A,
  p,q,p1,p2,q1 for Element of QC-WFF(A);
reserve s,t for bound_QC-variable of A;
reserve F,G,H,H1 for Element of QC-WFF(A);

theorem
  H is disjunctive implies H is conditional & H is negative &
  the_argument_of H is conjunctive & the_left_argument_of the_argument_of H is
  negative & the_right_argument_of the_argument_of H is negative
proof
  given F,G such that
A1: H = F 'or' G;
  F 'or' G = 'not' F => G;
  hence H is conditional by A1;
  thus H is negative by A1;
A2: the_argument_of H = 'not' F '&' 'not' G by A1,Th1;
  hence the_argument_of H is conjunctive;
  the_left_argument_of the_argument_of H = 'not' F & the_right_argument_of
  the_argument_of H = 'not' G by A2,Th4;
  hence thesis;
end;
