let i be Nat; :: thesis: for p being Point of (TOP-REAL 2)
for G being Go-board st 1 <= i & i + 1 <= len G holds
LSeg ((((1 / 2) * ((G * (i,1)) + (G * ((i + 1),1)))) - |[0,1]|),p) meets Int (cell (G,i,0))
let p be Point of (TOP-REAL 2); :: thesis: for G being Go-board st 1 <= i & i + 1 <= len G holds
LSeg ((((1 / 2) * ((G * (i,1)) + (G * ((i + 1),1)))) - |[0,1]|),p) meets Int (cell (G,i,0))
let G be Go-board; :: thesis: ( 1 <= i & i + 1 <= len G implies LSeg ((((1 / 2) * ((G * (i,1)) + (G * ((i + 1),1)))) - |[0,1]|),p) meets Int (cell (G,i,0)) )
assume A1: ( 1 <= i & i + 1 <= len G ) ; :: thesis: LSeg ((((1 / 2) * ((G * (i,1)) + (G * ((i + 1),1)))) - |[0,1]|),p) meets Int (cell (G,i,0))

now :: thesis: ex a being Element of the carrier of (TOP-REAL 2) st
( a in LSeg ((((1 / 2) * ((G * (i,1)) + (G * ((i + 1),1)))) - |[0,1]|),p) & a in Int (cell (G,i,0)) )

take a = ((1 / 2) * ((G * (i,1)) + (G * ((i + 1),1)))) - |[0,1]|; :: thesis: ( a in LSeg ((((1 / 2) * ((G * (i,1)) + (G * ((i + 1),1)))) - |[0,1]|),p) & a in Int (cell (G,i,0)) )
thus a in LSeg ((((1 / 2) * ((G * (i,1)) + (G * ((i + 1),1)))) - |[0,1]|),p) by RLTOPSP1:68; :: thesis: a in Int (cell (G,i,0))
thus a in Int (cell (G,i,0)) by A1, Th33; :: thesis: verum

end;

hence LSeg ((((1 / 2) * ((G * (i,1)) + (G * ((i + 1),1)))) - |[0,1]|),p) meets Int (cell (G,i,0)) by XBOOLE_0:3; :: thesis: verum