let i, j, k be 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 by A1, MATRIX_0:32;
A4: i <= len G by A1, MATRIX_0:32;
then A5: ( i < len G or i = len G ) by XXREAL_0:1;
( 1 <= j & j <= width G ) by A1, MATRIX_0:32;
then (G * (i,j)) `1 = (G * (i,1)) `1 by A3, A4, GOBOARD5:2
.= (G * (i,k)) `1 by A2, A3, A4, GOBOARD5:2 ;
hence (G * (i,j)) `1 <= (G * ((len G),k)) `1 by A2, A3, A5, GOBOARD5:3; :: thesis: verum