reserve x,y for set,
  i for Nat;
reserve V for non empty CLSStruct,
  u,v,v1,v2,v3 for VECTOR of V,
  A for Subset of V,
  l, l1, l2 for C_Linear_Combination of A,
  x,y,y1,y2 for set,
  a,b for Complex,
  F for FinSequence of the carrier of V,
  f for Function of the carrier of V, COMPLEX;
reserve K,L,L1,L2,L3 for C_Linear_Combination of V;

theorem Th26:
  L is C_Linear_Combination of A implies a * L is C_Linear_Combination of A
proof
  assume
A1: L is C_Linear_Combination of A;
A2: now
    assume a <> 0c;
    then Carrier (a * L) = Carrier L by Th24;
    hence thesis by A1,Def4;
  end;
  a = 0c implies a*L = ZeroCLC V by Th25;
  hence thesis by A2,Th4;
end;
