let i, j, k be Element of NAT ; :: thesis: for G being Go-board st [i,j] in Indices G & 1 <= k & k <= len G holds
(G * i,j) `2 <= (G * k,(width G)) `2
let G be Go-board; :: thesis: ( [i,j] in Indices G & 1 <= k & k <= len G implies (G * i,j) `2 <= (G * k,(width G)) `2 )
assume that
A1: [i,j] in Indices G and
A2: ( 1 <= k & k <= len G ) ; :: thesis: (G * i,j) `2 <= (G * k,(width G)) `2
A3: 1 <= j by A1, MATRIX_1:39;
A4: j <= width G by A1, MATRIX_1:39;
then A5: ( j < width G or j = width G ) by XXREAL_0:1;
( 1 <= i & i <= len G ) by A1, MATRIX_1:39;
then (G * i,j) `2 = (G * 1,j) `2 by A3, A4, GOBOARD5:2
.= (G * k,j) `2 by A2, A3, A4, GOBOARD5:2 ;
hence (G * i,j) `2 <= (G * k,(width G)) `2 by A2, A3, A5, GOBOARD5:5; :: thesis: verum