reserve n for Nat;

theorem Th39:
  for M be Go-board for f be S-Sequence_in_R2 st f is_sequence_on
M for p be Point of TOP-REAL 2 st p in rng f holds L_Cut(f,p) is_sequence_on M
proof
  let M be Go-board;
  let f be S-Sequence_in_R2;
  assume
A1: f is_sequence_on M;
  let p be Point of TOP-REAL 2;
  assume p in rng f;
  then L_Cut(f,p) = mid(f,p..f,len f) by Th37;
  hence thesis by A1,JORDAN1H:27;
end;
