reserve x,y for set;
reserve G for Graph;
reserve vs,vs9 for FinSequence of the carrier of G;
reserve IT for oriented Chain of G;
reserve N for Nat;
reserve n,m,k,i,j for Nat;
reserve r,r1,r2 for Real;
reserve X for non empty set;

theorem
  for f being FinSequence of TOP-REAL 2 st f is s.n.c. holds f is s.c.c.
proof
  let f be FinSequence of TOP-REAL 2;
  assume f is s.n.c.;
  then
  for i,j st i+1 < j & (i > 1 & j < len f or j+1 < len f) holds LSeg(f,i)
  misses LSeg(f,j) by TOPREAL1:def 7;
  hence thesis by GOBOARD5:def 4;
end;
