# How to check that exceptional sequence of vector bundles on Fano variety is helix foundation

Let $$X$$ be smooth Fano variety with $$\operatorname{Pic}(X) = \mathbb{Z}$$ of dimension $$m$$ with canonical class $$K$$, and $$E_0,...,E_n$$ is exceptional sequence of $$(n+1)$$ vector bundles in $$D^b(Coh(X))$$. Define inductively $$E_{n+i} = R_{} E_i$$ and $$E_{-i} = L_{} E_{-i+n}$$ where $$R_{C} A$$ and $$L_C A$$ is left and right mutations of object $$A$$ through category $$C$$. In "Representation of associative algebras and coherent sheaves" in theorem 4.2 Bondal states

Collection $$E_0,...,E_n$$ full iff $$\forall i E_{i+n+1} = E_i \otimes K[-m]$$

Is it sufficient to check only that $$E_{n+1} = E_0 \otimes K[-m]$$ or I really have to check every $$i$$? More vague question: how could I check that some exceptional collection of vector bundles is in fact full by finite number of computations?

It is not enough to check only $$E_0$$, but checking $$E_0,\dots,E_n$$ is enough.