theorem
 for p being PartState of S, i,j being Nat
 holds DecIC(DecIC(p,i),j) = DecIC(p,i+j)
 proof let p be PartState of S, i,j being Nat;
  thus DecIC(DecIC(p,i),j)
        = p +* Start-At(IC p-'i,S) +* Start-At(IC p -' i -' j,S) by Th65
       .= p +* Start-At(IC p-'i,S) +* Start-At(IC p -' (i + j),S) by NAT_2:30
       .= DecIC(p,i+j) by FUNCT_4:114;
 end;
