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 Th46:
  for f being S-Sequence_in_R2 st p in rng f & p..f <> 1 holds f-:
  p is being_S-Seq
proof
  let f be S-Sequence_in_R2 such that
A1: p in rng f and
A2: p..f <> 1;
  thus f-:p is one-to-one;
  1 <= p..f by A1,FINSEQ_4:21;
  then 1 < p..f by A2,XXREAL_0:1;
  then 1+1 <= p..f by NAT_1:13;
  hence len(f-:p) >= 2 by A1,FINSEQ_5:42;
  thus thesis;
end;
