reserve P for Subset of TOP-REAL 2,
  f,f1,f2,g for FinSequence of TOP-REAL 2,
  p,p1,p2,q,q1,q2 for Point of TOP-REAL 2,
  r1,r2,r19,r29 for Real,
  i,j,k,n for Nat;

theorem Th34:
  p in rng f & f is s.n.c. implies f:-p is s.n.c.
proof
  assume p in rng f;
  then ex i being Element of NAT st i+1 = p..f & f:-p = f/^i by FINSEQ_5:49;
  hence thesis;
end;
