let i, j, k be Element of NAT ; :: thesis: for G being Go-board st [i,j] in Indices G & 1 <= k & k <= width G holds
(G * i,j) `1 <= (G * (len G),k) `1
let G be Go-board; :: thesis: ( [i,j] in Indices G & 1 <= k & k <= width G implies (G * i,j) `1 <= (G * (len G),k) `1 )
assume that
A1: [i,j] in Indices G and
A2: ( 1 <= k & k <= width G ) ; :: thesis: (G * i,j) `1 <= (G * (len G),k) `1
A3: ( 1 <= i & i <= len G & 1 <= j & j <= width G ) by A1, MATRIX_1:39;
then A4: (G * i,j) `1 = (G * i,1) `1 by GOBOARD5:3
.= (G * i,k) `1 by A2, A3, GOBOARD5:3 ;
( i < len G or i = len G ) by A3, XXREAL_0:1;
hence (G * i,j) `1 <= (G * (len G),k) `1 by A2, A3, A4, GOBOARD5:4; :: thesis: verum