let i, j, k be 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 that
A1: 1 <= j and
A2: j <= width G and
A3: 1 <= i and
A4: i <= k and
A5: k <= len G ; :: thesis: (G * (i,j)) `1 <= (G * (k,j)) `1
per cases ( i < k or i = k ) by A4, 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, A2, A3, A5, GOBOARD5:3; :: 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;