let G be Go-board; :: thesis: for j, k, j1, k1 being Element of NAT st 1 <= j & j <= j1 & j1 <= k1 & k1 <= k & k <= width G holds
LSeg (G * (Center G),j1),(G * (Center G),k1) c= LSeg (G * (Center G),j),(G * (Center G),k)
let j, k, j1, k1 be Element of NAT ; :: thesis: ( 1 <= j & j <= j1 & j1 <= k1 & k1 <= k & k <= width G implies LSeg (G * (Center G),j1),(G * (Center G),k1) c= LSeg (G * (Center G),j),(G * (Center G),k) )
assume that
A1: 1 <= j and
A2: j <= j1 and
A3: j1 <= k1 and
A4: k1 <= k and
A5: k <= width G ; :: thesis: LSeg (G * (Center G),j1),(G * (Center G),k1) c= LSeg (G * (Center G),j),(G * (Center G),k)
A6: Center G <= len G by JORDAN1B:14;
1 <= Center G by JORDAN1B:12;
hence LSeg (G * (Center G),j1),(G * (Center G),k1) c= LSeg (G * (Center G),j),(G * (Center G),k) by A1, A2, A3, A4, A5, A6, Th7; :: thesis: verum