Yeah, this could be clearer. The point is that 1/(c(v+ + w−))*(v+ + w−) and 1/(c(v+ + w−))*(v- + w+) are formal sums of elements of L. These formal sums have positive coefficients which sum to 1, so they represent convex combinations. But their not equal as formal sums, only the results of applying the convex combination operation of L are equal.
Yeah, this could be clearer. The point is that 1/(c(v+ + w−))*(v+ + w−) and 1/(c(v+ + w−))*(v- + w+) are formal sums of elements of L. These formal sums have positive coefficients which sum to 1, so they represent convex combinations. But their not equal as formal sums, only the results of applying the convex combination operation of L are equal.