let j be Element of NAT ; :: thesis: for G being V9() Matrix of (TOP-REAL 2) st G is Y_equal-in-column & 1 <= j & j < width G holds
h_strip G,j = { |[r,s]| where r, s is Real : ( (G * 1,j) `2 <= s & s <= (G * 1,(j + 1)) `2 ) }
let G be V9() Matrix of (TOP-REAL 2); :: thesis: ( G is Y_equal-in-column & 1 <= j & j < width G implies h_strip G,j = { |[r,s]| where r, s is Real : ( (G * 1,j) `2 <= s & s <= (G * 1,(j + 1)) `2 ) } )
assume A1: G is Y_equal-in-column ; :: thesis: ( not 1 <= j or not j < width G or h_strip G,j = { |[r,s]| where r, s is Real : ( (G * 1,j) `2 <= s & s <= (G * 1,(j + 1)) `2 ) } )
assume A2: ( 1 <= j & j < width G ) ; :: thesis: h_strip G,j = { |[r,s]| where r, s is Real : ( (G * 1,j) `2 <= s & s <= (G * 1,(j + 1)) `2 ) }
0 <> len G by GOBOARD1:def 5;
then 1 <= len G by NAT_1:14;
hence h_strip G,j = { |[r,s]| where r, s is Real : ( (G * 1,j) `2 <= s & s <= (G * 1,(j + 1)) `2 ) } by A1, A2, GOBOARD5:6; :: thesis: verum