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 Th10:
  G is non empty-yielding X_equal-in-line & 1 <= j & j <= width G
  implies v_strip(G,0) = { |[r,s]| : r <= G*(1,j)`1 }
proof
  assume that
A1: G is non empty-yielding X_equal-in-line and
A2: 1 <= j and
A3: j <= width G;
  set A = { |[r,s]| : G*(1,j)`1 >= r };
A4: 0 <> len G by A1,MATRIX_0:def 10;
  then
A5: 0 < len G;
  1 <= len G by A4,NAT_1:14;
  then G*(1,j)`1 = G*(1,1)`1 by A1,A2,A3,Th2;
  then A = { |[r,s]| : G*(1,1+0)`1 >= r };
  hence thesis by A5,Def1;
end;
