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In the proof of Lemma 1.2 of [1] one case was missing and so the assertion of the lemma is not correct as it is stated in [1]. More precisely, the lower bound on |l ∩ B| in the lemma is not correct. We prove a new version of the lemma with the correct lower bound. The lemma was used several times in [1], but only the proof of Proposition 3.2 does not remain true with the new bound. We therefore give a new proof of Proposition 3.2 using the correct and weaker version of Lemma 1.1. As a matter of fact, the two main results in [1] (stated in the introduction) remain true.

New results on covers and partial spreads of polar spaces