inductive exT (A:Type) (P:A→CProp) : CProp ≝
ex_introT: ∀w:A. P w → exT A P.
-
-notation "\ll term 19 a, break term 19 b \gg"
-with precedence 90 for @{'dependent_pair $a $b}.
-interpretation "dependent pair" 'dependent_pair a b =
- (ex_introT _ _ a b).
interpretation "CProp exists" 'exists \eta.x = (exT _ x).
interpretation "dependent pair" 'dependent_pair a b =
(ex_introT _ _ a b).
-
definition pi1exT ≝ λA,P.λx:exT A P.match x with [ex_introT x _ ⇒ x].
definition pi2exT ≝
λA,P.λx:exT A P.match x return λx.P (pi1exT ?? x) with [ex_introT _ p ⇒ p].