reserve a,b,r for Real;
reserve A for non empty set;
reserve X,x for set;
reserve f,g,F,G for PartFunc of REAL,REAL;
reserve n for Element of NAT;

theorem Th8:
  (for x be set st x in X holds g.x <> 0) &
  f is_differentiable_on X & g is_differentiable_on X implies
  f/g is_differentiable_on X
proof
  assume that
A1: for x be set st x in X holds g.x <> 0 and
A2: f is_differentiable_on X and
A3: g is_differentiable_on X;
  reconsider Z = X as Subset of REAL by A2,FDIFF_1:8;
  reconsider Z as open Subset of REAL by A2,FDIFF_1:10;
  for x be Real st x in Z holds g.x <> 0 by A1;
  hence thesis by A2,A3,FDIFF_2:21;
end;
