any others that we can.

[sitifan]

We may assume any propositions we like provided they are all consistent; and we may prove from these propositions any others that we can. (Basic Geometry, by Birkhoff and Beatley, page 19)

We can what? Which verb is omitted after can?
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[GoesStation]

"Prove", I guess. You can't use consistent propositions to prove false propositions. I think it's a clumsy sentence.