reserve FS for non empty doubleLoopStr;
reserve F for Field;
reserve R for Abelian add-associative right_zeroed right_complementable non
  empty addLoopStr,
  x, y, z for Scalar of R;
reserve SF for Skew-Field,
  x, y, z for Scalar of SF;
reserve R, R1, R2 for Ring;

theorem
  for V being non empty BiModStr over R1,R2 holds (for x,y being Scalar
of R1 for p,q being Scalar of R2 for v,w being Vector of V holds x*(v+w) = x*v+
x*w & (x+y)*v = x*v+y*v & (x*y)*v = x*(y*v) & (1_R1)*v = v & (v+w)*p = v*p+w*p
& v*(p+q) = v*p+v*q & v*(q*p) = (v*q)*p & v*(1_R2) = v & x*(v*p) = (x*v)*p) iff
  V is RightMod-like vector-distributive scalar-distributive
  scalar-associative scalar-unital BiMod-like;
