theorem Th9:
  G is non empty-yielding X_equal-in-line & 1 <= j & j <= width G
  implies v_strip(G,len G) = { |[r,s]| : G*(len G,j)`1 <= r }
proof
  assume that
A1: G is non empty-yielding X_equal-in-line and
A2: 1 <= j and
A3: j <= width G;
  len G <> 0 by A1,MATRIX_0:def 10;
  then 1 <= len G by NAT_1:14;
  then G*(len G,j)`1 = G*(len G,1)`1 by A1,A2,A3,Th2;
  hence thesis by Def1;
end;
