Why do we need 2F prepare certificates instead of just F+1 in PBFT?

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Why do we need 2F prepare certificates instead of just F+1 in PBFT?

I started reading PBFT and I could not understand: why do we need 2F prepare certificates?

The client needs only F + 1 replies, not 2F, so why can't the same rule be applicable in the prepare phase of the protocol?

Same question in the commit phase, but this time it is even weirder: we need at least 2F + 1, again why not only F + 1, I just know that the quorum intersection must be more than 2F + 1 but we only need F + 1 replies from that quorum intersection as far as I know.

Source: Why do we need 2F prepare certificates instead of just F+1 in PBFT?