definition pi2exP ≝
λA,P.λx:exP A P.match x return λx.P (pi1exP ?? x) with [ex_introP _ p ⇒ p].
-interpretation "exT \fst" 'pi1 = (pi1exP _ _).
-interpretation "exT \fst" 'pi1a x = (pi1exP _ _ x).
-interpretation "exT \fst" 'pi1b x y = (pi1exP _ _ x y).
-interpretation "exT \snd" 'pi2 = (pi2exP _ _).
-interpretation "exT \snd" 'pi2a x = (pi2exP _ _ x).
-interpretation "exT \snd" 'pi2b x y = (pi2exP _ _ x y).
+interpretation "exP \fst" 'pi1 = (pi1exP _ _).
+interpretation "exP \fst" 'pi1a x = (pi1exP _ _ x).
+interpretation "exP \fst" 'pi1b x y = (pi1exP _ _ x y).
+interpretation "exP \snd" 'pi2 = (pi2exP _ _).
+interpretation "exP \snd" 'pi2a x = (pi2exP _ _ x).
+interpretation "exP \snd" 'pi2b x y = (pi2exP _ _ x y).
inductive exT23 (A:Type) (P:A→CProp) (Q:A→CProp) (R:A→A→CProp) : CProp ≝