let i1, i2, j1, j2 be Nat; :: thesis: 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; :: thesis: ( 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 ; :: thesis: (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; :: thesis: verum