
theorem Th11:
  for C be Simple_closed_curve for n be Nat st n
  is_sufficiently_large_for C holds C c= LeftComp Span(C,n)
proof
  let C be Simple_closed_curve;
  let n be Nat;
  assume
A1: n is_sufficiently_large_for C;
  let c be object;
  set f = Span(C,n);
  assume
A2: c in C;
  C misses L~f by A1,Th8;
  then
A3: not c in L~f by A2,XBOOLE_0:3;
  C misses RightComp f by A1,Th10;
  then not c in RightComp f by A2,XBOOLE_0:3;
  hence thesis by A2,A3,GOBRD14:18;
end;
