"This is usually shortened to X, Y ⊢ X ∧ Y based on the assumption that everything to the left of the turnstile is assumed to have already been judged to be true. Such a rule can be pronounced as follows: in a context in which you have already judged X and Y to be true you can always conclude that X ∧ Y is true." --> Does this mean that just stating X or just stating Y means that those are true, or does it mean that X is just equal to X? Is it circular, and will the meaning always be this way for inference rules? #26
The comma doesn't mean that only one is required. Think of it as listing all the things you know to be true (or need to know). If you know X is true and you know Y is true only then can you say that X ∧ Y (read this as X and Y) is true
The comma doesn't mean that only one is required. Think of it as listing all the things you know to be true (or need to know). If you know
X
is true and you know Y is true only then can you say thatX ∧ Y
(read this as X and Y) is true