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The lead-in sentence is odd:
Just as there are two notions of judgmental equality in dependent type theory, judgmental equality of terms and judgmental equality of types, there are two types in dependent type theory
Probably you mean instead something like
there are two kinds of identifications
And then next:
Typal equality of [X] is the [Y]-type
probably is meant to read
Typal equality of [X] is reflected by [Y]-types
or similar.
That’s much better, thanks!
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