nqed.
(*
+alias symbol "covers" (instance 0) = "covers".
+alias symbol "covers" (instance 2) = "covers".
+alias symbol "covers" (instance 1) = "covers set".
ntheorem covers_elim2:
∀A: axiom_set. ∀U:Ω^A.∀P: A → CProp[0].
(∀a:A. a ∈ U → P a) →
##]
nqed.
+STOP
+
definition leq ≝ λA:axiom_set.λa,b:A. a ◃ {y|b=y}.
interpretation "covered by one" 'leq a b = (leq ? a b).