reserve x,y for set;
reserve a,b for Real;
reserve i,j for Integer;
reserve V for RealLinearSpace;
reserve W1,W2,W3 for Subspace of V;
reserve v,v1,v2,v3,u,w,w1,w2,w3 for VECTOR of V;
reserve A,B,C for Subset of V;
reserve L,L1,L2 for Linear_Combination of V;
reserve l,l1,l2 for Linear_Combination of A;

theorem Th4:
  a = i implies a*l = i*l
proof
  assume A1:a=i;
  for v be VECTOR of V holds (i*l).v = a * l.v by A1,Def1;
  hence thesis by RLVECT_2:def 11;
end;
