reserve a,b for Complex;
reserve V,X,Y for ComplexLinearSpace;
reserve u,u1,u2,v,v1,v2 for VECTOR of V;
reserve z,z1,z2 for Complex;
reserve V1,V2,V3 for Subset of V;
reserve W,W1,W2 for Subspace of V;
reserve x for set;
reserve w,w1,w2 for VECTOR of W;

theorem Th33:
  w = v implies z * w = z * v
proof
  reconsider z as Element of COMPLEX by XCMPLX_0:def 2;
  z * w = ((the Mult of V) | [:COMPLEX, the carrier of W:]).[z,w] by Def8;
  hence thesis by FUNCT_1:49;
end;
