for f being non constant standard special_circular_sequence
for g being special FinSequence of (TOP-REAL 2) st f,g are_in_general_position holds
for k being Nat st 1 <= k & k + 1 <= len g holds
( card ((L~ f) /\ (LSeg (g,k))) is even Element of NAT iff ex C being Subset of (TOP-REAL 2) st
( C is_a_component_of (L~ f) ` & g . k in C & g . (k + 1) in C ) )