record Class: Type \def {
class:> Type;
- cin : class \to Prop;
- cle1 : class \to class \to Prop
+ cin: class \to Prop;
+ cle1: class \to class \to Prop
}.
-inductive ceq (C:Class) (c1:C): C \to Prop \def
- | ceq_refl: cin ? c1 \to ceq ? c1 c1
- | ceq_sing_r: \forall c2,c3.
- ceq ? c1 c2 \to cin ? c3 \to cle1 ? c2 c3 \to ceq ? c1 c3
- | ceq_sing_l: \forall c2,c3.
- ceq ? c1 c2 \to cin ? c3 \to cle1 ? c3 c2 \to ceq ? c1 c3.
+inductive cle (C:Class) (c1:C): C \to Prop \def
+ | cle_refl: cin ? c1 \to cle ? c1 c1
+ | ceq_sing: \forall c2,c3.
+ cle ? c1 c2 \to cin ? c3 \to cle1 ? c2 c3 \to cle ? c1 c3.
+
+inductive ceq (C:Class) (c1:C) (c2:C): Prop \def
+ | ceq_intro: cle ? c1 c2 \to cle ? c2 c1 \to ceq ? c1 c2.