Module Type Protothetic (dolce:DOLCE_root).
(************************** Meta-rules of Protothetic in Coq ***************************)
Parameter eqP : Prop -> Prop -> Prop.
Notation "a ≡≡ b" := (eqP a b)  (at level 80).

Axiom A1 :forall p q r, (((p ≡≡ r) ≡≡ (q ≡≡ p)) ≡≡ (r ≡≡ q)).
Axiom A2 :forall p q r, ((p ≡≡ (q ≡≡ r)) ≡≡ ((p ≡≡ q) ≡≡ r)).