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

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

take a = (1 / 2) * ((G * (i,j)) + (G * ((i + 1),(j + 1)))); :: thesis: ( a in LSeg (((1 / 2) * ((G * (i,j)) + (G * ((i + 1),(j + 1))))),p) & a in Int (cell (G,i,j)) )
thus a in LSeg (((1 / 2) * ((G * (i,j)) + (G * ((i + 1),(j + 1))))),p) by RLTOPSP1:68; :: thesis: a in Int (cell (G,i,j))
thus a in Int (cell (G,i,j)) by A1, Th31; :: thesis: verum

end;

hence LSeg (((1 / 2) * ((G * (i,j)) + (G * ((i + 1),(j + 1))))),p) meets Int (cell (G,i,j)) by XBOOLE_0:3; :: thesis: verum