begin{align*}
phileft(sum_{j=1}^{r}c^{j}(e)t_{j}(p) right)
&=  phileft(sum_{j=1}^{r} left(b^{j}circpi  right)(e)t_{j}(p)right),
\
text{or}qquad sum_{j=1}^{r}c^{j}(e)phi(t_{j}(e))
&=  sum_{j=1}^{r} left(b^{j}circpi right)(e)phi(t_{j}(p)),
 \
 text{or}qquad  sum_{j=1}^{r}c^{j}(e)(p,e_{j})
 &= sum_{j=1}^{r}  left(b^{j}circpi right)(e)(p,e_{j}) ,
 \
 text{or}qquad left(p, sum_{j=1}^{r}c^{j}(e)e_{j}  right)
  &= left(p, sum_{j=1}^{r}left(b^{j}circpi right)(e)e_{j} right).
 end{align*}