Comments (3)
I think it's common to define validity of context and then say that all contexts appearing in all rules are assumed to be valid. And there is probably a meta-theorem stating that conclusions of rules preserve validity of contexts, but I don't remember seeing one.
from plutus.
Yes, the other two rules should have "valid" at the bottom.
Roman is correct. We want lemmas such as:
if \Gamma valid and \Gamma \vdash x \ni A then \Gamma \vdash A :: (type)
Sometimes, there are extra hypotheses in \Gamma \vdash x \ni A to guarantee
if \Gamma \vdash x \ni A then \Gamma valid
but this system has not been formulated that way.
from plutus.
Done.
from plutus.
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from plutus.