theorem :: GOBOARD1:36

for G being Go-board
for f being FinSequence of (TOP-REAL 2) st f is_sequence_on G & (rng f) /\ (rng (Col (G,1))) <> {} & (rng f) /\ (rng (Col (G,(width G)))) <> {} holds
ex g being FinSequence of (TOP-REAL 2) st
( rng g c= rng f & g /. 1 in rng (Col (G,1)) & g /. (len g) in rng (Col (G,(width G))) & 1 <= len g & g is_sequence_on G )