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;
reserve e,e1,e2 for Element of C_LinComb V;

theorem
  for V being non empty CLSStruct, M being Subset of V, N being convex
  Subset of V st M c= N holds conv M c= N
proof
  let V be non empty CLSStruct;
  let M be Subset of V;
  let N be convex Subset of V;
  assume M c= N;
  then N in Convex-Family M by Def25;
  hence thesis by SETFAM_1:3;
end;
