Inf and sup methods in Sage

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In an exercice using Sage, I would need a method that returns the sup/inf of an interval, in such a way as to be able to use that value futher down in the code. Someting like $\mathtt{inf}([x>3])$ returns $3$ $-$ which looks ridiculous stated that way, but the interval would be given using the solve method on previously defined functions. Is there any (simple) way to do that?

Thanks