I am reading Chriswell & Hodges which says (p. 7)
A sequent is an expression
$(Γ \vdash ψ)$
where $ψ$ is a statement and $Γ$ is a set of statements. The sequent $(Γ \vdash ψ)$ means
(2.2) There is a proof whose conclusion is $ψ$ and whose undischarged assumptions are all in the set $Γ$.
When (2.2) is true, we say that the sequent is correct.
Why are the authors using 'true' and 'correct' instead of just 'true'? Is there some difference between the meaning of the two words?