let j be Nat; :: thesis: for G being empty-yielding 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 empty-yielding 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 ) } )
0 <> len G by MATRIX_0:def 10;
then A2: 1 <= len G by NAT_1:14;
assume ( 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 ) }
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, GOBOARD5:5; :: thesis: verum