for Al being QC-alphabet
for k being Nat
for A being non empty set
for v being Element of Valuations_in (Al,A)
for P being QC-pred_symbol of k,Al
for ll being CQC-variable_list of k,Al
for Sub being CQC_Substitution of Al holds (v . (Val_S (v,(Sub_P (P,ll,Sub))))) *' ll = v *' (CQC_Subst (ll,Sub))