reserve p,q for Point of TOP-REAL 2,
  i,i1,i2,j,j1,j2,k for Nat,
  r,s for Real,
  G for Matrix of TOP-REAL 2;

theorem Th7:
  G is non empty-yielding Y_equal-in-column & 1 <= i & i <= len G
  implies h_strip(G,0) = { |[r,s]| : s <= G*(i,1)`2 }
proof
  assume that
A1: G is non empty-yielding Y_equal-in-column and
A2: 1 <= i and
A3: i <= len G;
  set A = { |[r,s]| : G*(i,1)`2 >= s };
A4: 0 <> width G by A1,MATRIX_0:def 10;
  then
A5: 0 < width G;
  1 <= width G by A4,NAT_1:14;
  then G*(i,1)`2 = G*(1,1)`2 by A1,A2,A3,Th1;
  then A = { |[r,s]| : G*(1,1+0)`2 >= s };
  hence thesis by A5,Def2;
end;
