let j be Element of NAT ; :: thesis: for G being Matrix of (TOP-REAL 2) st not G is empty-yielding & G is X_equal-in-line & 1 <= j & j <= width G holds
v_strip G,(len G) = { |[r,s]| where r, s is Real : (G * (len G),j) `1 <= r }
let G be Matrix of (TOP-REAL 2); :: thesis: ( not G is empty-yielding & G is X_equal-in-line & 1 <= j & j <= width G implies v_strip G,(len G) = { |[r,s]| where r, s is Real : (G * (len G),j) `1 <= r } )
assume that
A1: ( not G is empty-yielding & G is X_equal-in-line ) and
A2: 1 <= j and
A3: j <= width G ; :: thesis: v_strip G,(len G) = { |[r,s]| where r, s is Real : (G * (len G),j) `1 <= r }
len G <> 0 by A1, GOBOARD1:def 5;
then 1 <= len G by NAT_1:14;
then (G * (len G),j) `1 = (G * (len G),1) `1 by A1, A2, A3, Th3;
hence v_strip G,(len G) = { |[r,s]| where r, s is Real : (G * (len G),j) `1 <= r } by Def1; :: thesis: verum