inductive exT22 (A:Type2) (P:A→CProp2) : CProp2 ≝
ex_introT22: ∀w:A. P w → exT22 A P.
-interpretation "CProp2 exists" 'exists \eta.x = (exT22 _ x).
+interpretation "CProp2 exists" 'exists \eta.x = (exT22 ? x).
definition pi1exT22 ≝ λA,P.λx:exT22 A P.match x with [ex_introT22 x _ ⇒ x].
definition pi2exT22 ≝
λA,P.λx:exT22 A P.match x return λx.P (pi1exT22 ?? x) with [ex_introT22 _ p ⇒ p].
-interpretation "exT22 \fst" 'pi1 = (pi1exT22 _ _).
-interpretation "exT22 \snd" 'pi2 = (pi2exT22 _ _).
-interpretation "exT22 \fst a" 'pi1a x = (pi1exT22 _ _ x).
-interpretation "exT22 \snd a" 'pi2a x = (pi2exT22 _ _ x).
-interpretation "exT22 \fst b" 'pi1b x y = (pi1exT22 _ _ x y).
-interpretation "exT22 \snd b" 'pi2b x y = (pi2exT22 _ _ x y).
+interpretation "exT22 \fst" 'pi1 = (pi1exT22 ? ?).
+interpretation "exT22 \snd" 'pi2 = (pi2exT22 ? ?).
+interpretation "exT22 \fst a" 'pi1a x = (pi1exT22 ? ? x).
+interpretation "exT22 \snd a" 'pi2a x = (pi2exT22 ? ? x).
+interpretation "exT22 \fst b" 'pi1b x y = (pi1exT22 ? ? x y).
+interpretation "exT22 \snd b" 'pi2b x y = (pi2exT22 ? ? x y).
inductive exT (A:Type0) (P:A→CProp0) : CProp0 ≝
ex_introT: ∀w:A. P w → exT A P.
-interpretation "CProp exists" 'exists \eta.x = (exT _ x).
+interpretation "CProp exists" 'exists \eta.x = (exT ? x).
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).
+ (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].
-interpretation "exT \fst" 'pi1 = (pi1exT _ _).
-interpretation "exT \fst a" 'pi1a x = (pi1exT _ _ x).
-interpretation "exT \fst b" 'pi1b x y = (pi1exT _ _ x y).
-interpretation "exT \snd" 'pi2 = (pi2exT _ _).
-interpretation "exT \snd a" 'pi2a x = (pi2exT _ _ x).
-interpretation "exT \snd b" 'pi2b x y = (pi2exT _ _ x y).
+interpretation "exT \fst" 'pi1 = (pi1exT ? ?).
+interpretation "exT \fst a" 'pi1a x = (pi1exT ? ? x).
+interpretation "exT \fst b" 'pi1b x y = (pi1exT ? ? x y).
+interpretation "exT \snd" 'pi2 = (pi2exT ? ?).
+interpretation "exT \snd a" 'pi2a x = (pi2exT ? ? x).
+interpretation "exT \snd b" 'pi2b x y = (pi2exT ? ? x y).
inductive exT23 (A:Type0) (P:A→CProp0) (Q:A→CProp0) (R:A→A→CProp0) : CProp0 ≝
ex_introT23: ∀w,p:A. P w → Q p → R w p → exT23 A P Q R.
definition pi2exT23 ≝
λA,P,Q,R.λx:exT23 A P Q R.match x with [ex_introT23 _ x _ _ _ ⇒ x].
-interpretation "exT2 \fst" 'pi1 = (pi1exT23 _ _ _ _).
-interpretation "exT2 \snd" 'pi2 = (pi2exT23 _ _ _ _).
-interpretation "exT2 \fst a" 'pi1a x = (pi1exT23 _ _ _ _ x).
-interpretation "exT2 \snd a" 'pi2a x = (pi2exT23 _ _ _ _ x).
-interpretation "exT2 \fst b" 'pi1b x y = (pi1exT23 _ _ _ _ x y).
-interpretation "exT2 \snd b" 'pi2b x y = (pi2exT23 _ _ _ _ x y).
+interpretation "exT2 \fst" 'pi1 = (pi1exT23 ? ? ? ?).
+interpretation "exT2 \snd" 'pi2 = (pi2exT23 ? ? ? ?).
+interpretation "exT2 \fst a" 'pi1a x = (pi1exT23 ? ? ? ? x).
+interpretation "exT2 \snd a" 'pi2a x = (pi2exT23 ? ? ? ? x).
+interpretation "exT2 \fst b" 'pi1b x y = (pi1exT23 ? ? ? ? x y).
+interpretation "exT2 \snd b" 'pi2b x y = (pi2exT23 ? ? ? ? x y).
inductive exT2 (A:Type0) (P,Q:A→CProp0) : CProp0 ≝
ex_introT2: ∀w:A. P w → Q w → exT2 A P Q.