let V be RealLinearSpace; :: thesis: for v1, v2, w being VECTOR of V st v1 - w = v2 - w holds
v1 = v2
let v1, v2, w be VECTOR of V; :: thesis: ( v1 - w = v2 - w implies v1 = v2 )
assume v1 - w = v2 - w ; :: thesis: v1 = v2
then - (v1 - w) = w - v2 by RLVECT_1:33;
then w - v1 = w - v2 by RLVECT_1:33;
hence v1 = v2 by RLVECT_1:23; :: thesis: verum