let i1, i2, j1, j2 be Nat; for G being Go-board st 1 <= j1 & j1 <= width G & 1 <= j2 & j2 <= width G & 1 <= i1 & i1 <= i2 & i2 <= len G holds
(G * (i1,j1)) `1 <= (G * (i2,j2)) `1
let G be Go-board; ( 1 <= j1 & j1 <= width G & 1 <= j2 & j2 <= width G & 1 <= i1 & i1 <= i2 & i2 <= len G implies (G * (i1,j1)) `1 <= (G * (i2,j2)) `1 )
assume that
A1:
( 1 <= j1 & j1 <= width G )
and
A2:
( 1 <= j2 & j2 <= width G )
and
A3:
( 1 <= i1 & i1 <= i2 )
and
A4:
i2 <= len G
; (G * (i1,j1)) `1 <= (G * (i2,j2)) `1
A5:
1 <= i2
by A3, XXREAL_0:2;
then (G * (i2,j1)) `1 =
(G * (i2,1)) `1
by A1, A4, GOBOARD5:2
.=
(G * (i2,j2)) `1
by A2, A4, A5, GOBOARD5:2
;
hence
(G * (i1,j1)) `1 <= (G * (i2,j2)) `1
by A1, A3, A4, SPRECT_3:13; verum