&\le c_1 D(m,n) + cD(m/2, n/4) + c_2m &(induction hypothesis)\cr
&\le c_1 D(m,n) + c/2\cdot D(m,n/2) + c_2m &(Corollary \ref{dttwice})\cr
&\le c_1 D(m,n) + c/2\cdot D(m,n) + 2c_2 D(m,n) &(Lemma \ref{dtbasic})\cr
&\le (c_1 + c/2 + 2c_2) \cdot D(m,n)&\cr
&\le cD(m,n). &(by setting $c=2c_1+4c_2$)\cr
}}$$
&\le c_1 D(m,n) + cD(m/2, n/4) + c_2m &(induction hypothesis)\cr
&\le c_1 D(m,n) + c/2\cdot D(m,n/2) + c_2m &(Corollary \ref{dttwice})\cr
&\le c_1 D(m,n) + c/2\cdot D(m,n) + 2c_2 D(m,n) &(Lemma \ref{dtbasic})\cr
&\le (c_1 + c/2 + 2c_2) \cdot D(m,n)&\cr
&\le cD(m,n). &(by setting $c=2c_1+4c_2$)\cr
}}$$