theorem Th4:
 for GF being commutative non degenerated
     Abelian add-associative right_zeroed right_complementable
     associative well-unital distributive non empty doubleLoopStr,
     V being scalar-distributive vector-distributive
   scalar-associative scalar-unital add-associative right_zeroed
     right_complementable Abelian non empty ModuleStr over GF,
     v1, v2 being Vector of V st
  {v1,v2} is linearly-independent holds v1 <> 0.V
proof
 let GF be commutative non degenerated
     Abelian add-associative right_zeroed right_complementable
     associative well-unital distributive non empty doubleLoopStr,
     V be scalar-distributive vector-distributive
   scalar-associative scalar-unital add-associative right_zeroed
     right_complementable Abelian non empty ModuleStr over GF,
     v1, v2 be Vector of V;
A1: v1 in {v1,v2} by TARSKI:def 2;
  assume {v1,v2} is linearly-independent;
  hence thesis by A1,Th2;
end;
