consider v being Vector of V, w being Vector of W such that

A1: f . (v,w) <> 0. K by Th40;

reconsider B = w + (RKer f) as Vector of (VectQuot (W,(RKer f))) by VECTSP10:23;

reconsider A = v + (LKer f) as Vector of (VectQuot (V,(LKer f))) by VECTSP10:23;

(QForm f) . (A,B) = f . (v,w) by Def22;

hence not QForm f is constant by A1, Th40; :: thesis: verum

A1: f . (v,w) <> 0. K by Th40;

reconsider B = w + (RKer f) as Vector of (VectQuot (W,(RKer f))) by VECTSP10:23;

reconsider A = v + (LKer f) as Vector of (VectQuot (V,(LKer f))) by VECTSP10:23;

(QForm f) . (A,B) = f . (v,w) by Def22;

hence not QForm f is constant by A1, Th40; :: thesis: verum