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 Th8:
  Z_Lin(A) c= the carrier of Lin(A)
proof
    let x be object;
    assume x in Z_Lin(A); then
    consider l1 being Linear_Combination of A such that
A1: x = Sum(l1) & rng l1 c= INT;
    x in Lin(A) by A1,RLVECT_3:14;
    hence thesis by STRUCT_0:def 5;
end;
