include "logic/pts.ma".
-ndefinition reflexive ≝ λT:Type[0].λP:T → T → CProp[0]. ∀x.P x x.
-ndefinition symmetric ≝ λT:Type[0].λP:T → T → CProp[0]. ∀x,y.P x y → P y x.
-ndefinition transitive ≝ λT:Type[0].λP:T → T → CProp[0]. ∀z,x,y. P x z → P z y → P x y.
+definition reflexive ≝ λT:Type[0].λP:T → T → CProp[0]. ∀x.P x x.
+definition symmetric ≝ λT:Type[0].λP:T → T → CProp[0]. ∀x,y.P x y → P y x.
+definition transitive ≝ λT:Type[0].λP:T → T → CProp[0]. ∀z,x,y. P x z → P z y → P x y.
-nrecord equivalence_relation (A:Type[0]) : Type[1] ≝
+record equivalence_relation (A:Type[0]) : Type[1] ≝
{ eq_rel:2> A → A → CProp[0];
refl: reflexive ? eq_rel;
sym: symmetric ? eq_rel;