let i, j, k be Nat; :: thesis: for G being Go-board st 1 <= j & j <= k & k <= width G & 1 <= i & i <= len G holds
(G * (i,j)) `2 <= (G * (i,k)) `2
let G be Go-board; :: thesis: ( 1 <= j & j <= k & k <= width G & 1 <= i & i <= len G implies (G * (i,j)) `2 <= (G * (i,k)) `2 )
assume that
A1: 1 <= j and
A2: j <= k and
A3: k <= width G and
A4: 1 <= i and
A5: i <= len G ; :: thesis: (G * (i,j)) `2 <= (G * (i,k)) `2

per cases ( j < k or j = k ) by A2, XXREAL_0:1;

suppose j < k ; :: thesis: (G * (i,j)) `2 <= (G * (i,k)) `2

hence (G * (i,j)) `2 <= (G * (i,k)) `2 by A1, A3, A4, A5, GOBOARD5:4; :: thesis: verum

end;

suppose j = k ; :: thesis: (G * (i,j)) `2 <= (G * (i,k)) `2

hence (G * (i,j)) `2 <= (G * (i,k)) `2 ; :: thesis: verum

end;

end;