\close
-\open logical_abbreviations \* [1] 2.3. *\
+\open logical_abbreviations \* [1] 2.3. 2.5. *\
+
+ \def "logical comprehension restricted to classifications"
+ CAll = [q:*Obj->*Prop] [x:*Obj] Cl(x) -> q(x)
+ : (*Obj -> *Prop) -> *Prop
+
+ \def "logical existence restricted to classifications"
+ CEx = [q:*Obj->*Prop] Ex([x:*Obj] And(Cl(x), q(x)))
+ : (*Obj -> *Prop) -> *Prop
+
+ \def "logical comprehension restricted to a classification"
+ EAll = [a:*Obj, q:*Obj->*Prop] [x:*Obj] Eta(x, a) -> q(x)
+ : *Obj => (*Obj -> *Prop) -> *Prop
+
+ \def "logical existence restricted to a classification"
+ EEx = [a:*Obj, q:*Obj->*Prop] Ex([x:*Obj] And(Eta(x, a), q(x)))
+ : *Obj => (*Obj -> *Prop) -> *Prop
+
+\close
+
+\open non_logical_abbreviations \* [1] 2.4. *\
+
+ \def "convergence of a term to an object"
+ Conv = [t:*Term] EX([y:*Obj] E(t, y)) : *Term -> *Prop
+
+ \def "term-term equivalence"
+ Eq = [t1:*Term, t2:*Term] [y:*Obj] Iff(E(t1, y), E(t2, y))
+ : *Term => *Term -> *Prop
\close