let j be Nat; for p being Point of (TOP-REAL 2)
for G being Go-board st 1 <= j & j + 1 <= width G holds
LSeg ((((1 / 2) * ((G * (1,j)) + (G * (1,(j + 1))))) - |[1,0]|),p) meets Int (cell (G,0,j))
let p be Point of (TOP-REAL 2); for G being Go-board st 1 <= j & j + 1 <= width G holds
LSeg ((((1 / 2) * ((G * (1,j)) + (G * (1,(j + 1))))) - |[1,0]|),p) meets Int (cell (G,0,j))
let G be Go-board; ( 1 <= j & j + 1 <= width G implies LSeg ((((1 / 2) * ((G * (1,j)) + (G * (1,(j + 1))))) - |[1,0]|),p) meets Int (cell (G,0,j)) )
assume A1:
( 1 <= j & j + 1 <= width G )
; LSeg ((((1 / 2) * ((G * (1,j)) + (G * (1,(j + 1))))) - |[1,0]|),p) meets Int (cell (G,0,j))
now ex a being Element of the carrier of (TOP-REAL 2) st
( a in LSeg ((((1 / 2) * ((G * (1,j)) + (G * (1,(j + 1))))) - |[1,0]|),p) & a in Int (cell (G,0,j)) )take a =
((1 / 2) * ((G * (1,j)) + (G * (1,(j + 1))))) - |[1,0]|;
( a in LSeg ((((1 / 2) * ((G * (1,j)) + (G * (1,(j + 1))))) - |[1,0]|),p) & a in Int (cell (G,0,j)) )thus
a in LSeg (
(((1 / 2) * ((G * (1,j)) + (G * (1,(j + 1))))) - |[1,0]|),
p)
by RLTOPSP1:68;
a in Int (cell (G,0,j))thus
a in Int (cell (G,0,j))
by A1, Th35;
verum end;
hence
LSeg ((((1 / 2) * ((G * (1,j)) + (G * (1,(j + 1))))) - |[1,0]|),p) meets Int (cell (G,0,j))
by XBOOLE_0:3; verum