let j, i, k be Element of NAT ; :: thesis: for G being Go-board st 1 <= j & j <= width G & 1 <= i & i <= k & k <= len G holds
(G * i,j) `1 <= (G * k,j) `1
let G be Go-board; :: thesis: ( 1 <= j & j <= width G & 1 <= i & i <= k & k <= len G implies (G * i,j) `1 <= (G * k,j) `1 )
assume A1: ( 1 <= j & j <= width G & 1 <= i & i <= k & k <= len G ) ; :: thesis: (G * i,j) `1 <= (G * k,j) `1

per cases ( i < k or i = k ) by A1, XXREAL_0:1;

suppose i < k ; :: thesis: (G * i,j) `1 <= (G * k,j) `1

hence (G * i,j) `1 <= (G * k,j) `1 by A1, GOBOARD5:4; :: thesis: verum

end;

suppose i = k ; :: thesis: (G * i,j) `1 <= (G * k,j) `1

hence (G * i,j) `1 <= (G * k,j) `1 ; :: thesis: verum

end;

end;