let i be Element of NAT ; :: thesis: for G being V9() Matrix of (TOP-REAL 2) st G is X_equal-in-line & 1 <= i & i < len G holds
v_strip G,i = { |[r,s]| where r, s is Real : ( (G * i,1) `1 <= r & r <= (G * (i + 1),1) `1 ) }
let G be V9() Matrix of (TOP-REAL 2); :: thesis: ( G is X_equal-in-line & 1 <= i & i < len G implies v_strip G,i = { |[r,s]| where r, s is Real : ( (G * i,1) `1 <= r & r <= (G * (i + 1),1) `1 ) } )
assume A1: G is X_equal-in-line ; :: thesis: ( not 1 <= i or not i < len G or v_strip G,i = { |[r,s]| where r, s is Real : ( (G * i,1) `1 <= r & r <= (G * (i + 1),1) `1 ) } )
assume A2: ( 1 <= i & i < len G ) ; :: thesis: v_strip G,i = { |[r,s]| where r, s is Real : ( (G * i,1) `1 <= r & r <= (G * (i + 1),1) `1 ) }
0 <> width G by GOBOARD1:def 5;
then 1 <= width G by NAT_1:14;
hence v_strip G,i = { |[r,s]| where r, s is Real : ( (G * i,1) `1 <= r & r <= (G * (i + 1),1) `1 ) } by A1, A2, GOBOARD5:9; :: thesis: verum