How to extract the second element of Sigma on the Calculus of Constructions?

问题

I'm attempting to do that as follows:

λ (A : *) ->
λ (B : (A -> *)) ->
λ (t : (∀ (r : *) -> (∀ (x : a) -> (B x) -> r)) -> r) ->
(t (B (t A (λ (x : A) -> λ (y : (B x)) -> x)))
    (λ (x : A) -> λ (y : (B x)) -> y))

Notice that, since the value returned by that function depends on a value inside the sigma itself, I need to extract that value. This code doesn't check, because, I believe, it fails to unify the type extracted from Sigma with the type inside it.

Is there any workaround?

来源：https://stackoverflow.com/questions/43957592/how-to-extract-the-second-element-of-sigma-on-the-calculus-of-constructions