notation "hvbox(x break ∈ A)" with precedence 60
for @{ 'member_of $x $A }.
-interpretation "Member of" 'member_of x A = (mk_member_of _ A x).
+interpretation "Member of" 'member_of x A = (mk_member_of ? A x).
notation "hvbox(x break ∉ A)" with precedence 60
for @{ 'not_member_of $x $A }.
-interpretation "Not member of" 'not_member_of x A = (Not (member_of _ A x)).
+interpretation "Not member of" 'not_member_of x A = (Not (member_of ? A x)).
definition emptyset : ∀X.set X ≝ λX:Type.λx:X.False.
notation "∅︀" with precedence 100 for @{ 'emptyset }.
-interpretation "Emptyset" 'emptyset = (emptyset _).
+interpretation "Emptyset" 'emptyset = (emptyset ?).
definition subset: ∀X. set X → set X → Prop≝ λX.λA,B:set X.∀x. x ∈ A → x ∈ B.
notation "hvbox(A break ⊆ B)" with precedence 60
for @{ 'subset $A $B }.
-interpretation "Subset" 'subset A B = (subset _ A B).
+interpretation "Subset" 'subset A B = (subset ? A B).
definition intersection: ∀X. set X → set X → set X ≝
λX.λA,B:set X.λx. x ∈ A ∧ x ∈ B.
notation "hvbox(A break ∩ B)" with precedence 70
for @{ 'intersection $A $B }.
-interpretation "Intersection" 'intersection A B = (intersection _ A B).
+interpretation "Intersection" 'intersection A B = (intersection ? A B).
definition union: ∀X. set X → set X → set X ≝ λX.λA,B:set X.λx. x ∈ A ∨ x ∈ B.
notation "hvbox(A break ∪ B)" with precedence 65
for @{ 'union $A $B }.
-interpretation "Union" 'union A B = (union _ A B).
+interpretation "Union" 'union A B = (union ? A B).
definition seq ≝ λX:Type.nat → X.
notation "hvbox(A \sub i)" with precedence 100
for @{ 'nth $A $i }.
-interpretation "nth" 'nth A i = (nth _ A i).
+interpretation "nth" 'nth A i = (nth ? A i).
definition countable_union: ∀X. seq (set X) → set X ≝
λX.λA:seq (set X).λx.∃j.x ∈ A \sub j.
notation "∪ \sub (ident i opt (: ty)) B" with precedence 65
for @{ 'big_union ${default @{(λ${ident i}:$ty.$B)} @{(λ${ident i}.$B)}}}.
-interpretation "countable_union" 'big_union η.t = (countable_union _ t).
+interpretation "countable_union" 'big_union η.t = (countable_union ? t).
definition complement: ∀X. set X \to set X ≝ λX.λA:set X.λx. x ∉ A.
notation "A \sup 'c'" with precedence 100
for @{ 'complement $A }.
-interpretation "Complement" 'complement A = (complement _ A).
+interpretation "Complement" 'complement A = (complement ? A).
definition inverse_image: ∀X,Y.∀f: X → Y.set Y → set X ≝
λX,Y,f,B,x. f x ∈ B.
notation "hvbox(f \sup (-1))" with precedence 100
for @{ 'finverse $f }.
-interpretation "Inverse image" 'finverse f = (inverse_image _ _ f).
+interpretation "Inverse image" 'finverse f = (inverse_image ? ? f).