Relation INVERTIBLE

• Defined in theory: Abstract-algebra
• Source code: abstract-algebra.lisp

Slots on this relation:

Instance-Of: Relation

Arity: 3

Equivalence Axioms:

(<=> (Invertible ?Op ?Id ?Domain)
     (Forall (?X)
             (=> (Instance-Of ?X ?Domain)
                 (Exists (?Y)
                         (And (Instance-Of ?Y ?Domain)
                              (= (Value ?Op ?X ?Y) ?Id)
                              (= (Value ?Op ?Y ?X) ?Id))))))

Other Related Axioms:

(<=> (Invertible ?Op ?Id ?Domain)
     (Forall (?X)
             (=> (Instance-Of ?X ?Domain)
                 (Exists (?Y)
                         (And (Instance-Of ?Y ?Domain)
                              (= (Value ?Op ?X ?Y) ?Id)
                              (= (Value ?Op ?Y ?X) ?Id))))))

(<=> (Group ?Domain ?Op ?Id)
     (And (Binary-Operator-On ?Op ?Domain)
          (Associative ?Op ?Domain)
          (Identity-Element-For ?Id ?Op ?Domain)
          (Invertible ?Op ?Id ?Domain)))