(* If A is something, then A is a singular *)

(* Specifications: *)
Lemma OntoT5 : forall A b, A ε b ⊃ A ε A.
(* characteristic thesis of the ontology  *)
Lemma OntoT6 : forall a A B, A ε B ∧ B ε a ⊃ B ε A.
Lemma OntoT7 : forall A B a, A ε B ∧ B ε a ⊃ A ε a.
(* contradictory name *)
Lemma OntoT8 : forall A, ¬(A ε empty).
(* empty name is not a singular *)
Lemma OntoT9 : ¬(empty ε empty).
(* it is false that any name is a singular - creativity *)
Lemma OntoT10 : ¬forall A, A ε A.
Lemma OntoT12 : forall A b, A ε (distinct b) ⊃ ¬(A ε b).
Lemma OntoT14 : forall A, A ε A ⊃ ¬forall b, ¬(A ε b).
Lemma OntoT17 : ¬exist_at_least empty.
Lemma OntoT18 : forall A a, A ε a ⊃ weak_inclusion A a.
Lemma OntoT21 : forall A B a, A ε B ∧ B ε a ⊃ singular_equality A B.
Lemma OntoT23 : forall a, weak_equality a a.
Lemma OntoT24 : forall a b, weak_equality a b ⊃ weak_equality b a.
Lemma OntoT25 : forall a b c, weak_equality a b ∧ weak_equality b c ⊃ weak_equality a c.
Lemma OntoT27 : forall a b, singular_equality a b ⊃ singular_equality b a.
Lemma OntoT28 : forall a b c, singular_equality a b ∧ singular_equality b c ⊃ singular_equality a c.
Parameter eq_N       : N -> N -> Prop.