reserve k,m,n for Element of NAT,
  i, j for Nat,
  a, b, c for object,
  X, Y, Z for set,
  D, D1, D2 for non empty set;
reserve p, q, r, s for FinSequence;
reserve t, u, v, w for GRZ-formula;
reserve R, R1, R2 for GRZ-rule;
reserve A, A1, A2 for non empty Subset of GRZ-formula-set;
reserve B, B1, B2 for Subset of GRZ-formula-set;
reserve P, P1, P2 for GRZ-formula-sequence;
reserve S, S1, S2 for GRZ-formula-finset;

theorem Th76:
  for t, u st t LD-= u holds 'not' t LD-= 'not' u
proof
  let t, u;
  set v = (t '=' u) '=' (('not' t) '=' ('not' u));
  assume t LD-= u;
  then A1: t '=' u is LD-provable;
  v is LD-provable;
  then ('not' t) '=' ('not' u) is LD-provable by A1, Th61;
  hence thesis;
end;
