let i be Nat; :: thesis: for G being Matrix of (TOP-REAL 2) st G is empty-yielding & G is Y_equal-in-column & 1 <= i & i <= len G holds
h_strip (G,(width G)) = { |[r,s]| where r, s is Real : (G * (i,(width G))) `2 <= s }
let G be Matrix of (TOP-REAL 2); :: thesis: ( G is empty-yielding & G is Y_equal-in-column & 1 <= i & i <= len G implies h_strip (G,(width G)) = { |[r,s]| where r, s is Real : (G * (i,(width G))) `2 <= s } )
assume that
A1: ( G is empty-yielding & G is Y_equal-in-column ) and
A2: 1 <= i and
A3: i <= len G ; :: thesis: h_strip (G,(width G)) = { |[r,s]| where r, s is Real : (G * (i,(width G))) `2 <= s }
width G <> 0 by A1, MATRIX_0:def 10;
then 1 <= width G by NAT_1:14;
then (G * (i,(width G))) `2 = (G * (1,(width G))) `2 by A1, A2, A3, Th1;
hence h_strip (G,(width G)) = { |[r,s]| where r, s is Real : (G * (i,(width G))) `2 <= s } by Def2; :: thesis: verum