
theorem
  for P being TolStr, D being Subset-Family of P
  for A, B being set holds [A,B] in pcs-general-power-TR(P,D) iff
  A in D & B in D &
  for a, b being Element of P st a in A & b in B holds a (--) b
proof
  let P be TolStr, D be Subset-Family of P;
  let A, B be set;
  thus [A,B] in pcs-general-power-TR(P,D) implies A in D & B in D &
  for a, b being Element of P st a in A & b in B holds a (--) b
  by Def46;
  assume that
A1: A in D and
A2: B in D and
A3: for a, b being Element of P st a in A & b in B holds a (--) b;
  for a, b being set st a in A & b in B holds [a,b] in the ToleranceRel of P
  by A1,A2,A3,Def7;
  hence thesis by A1,A2,Def46;
end;
