+(* exists *******************************************************************)
+
+notation "hvbox(∃ _ break . p)"
+ with precedence 20
+for @{'exists $p }.
+
+notation < "hvbox(\exists ident i : ty break . p)"
+ right associative with precedence 20
+for @{'exists (\lambda ${ident i} : $ty. $p) }.
+
+notation < "hvbox(\exists ident i break . p)"
+ with precedence 20
+for @{'exists (\lambda ${ident i}. $p) }.
+
+(*
notation < "hvbox(\exists ident i opt (: ty) break . p)"
right associative with precedence 20
for @{ 'exists ${default
@{\lambda ${ident i} : $ty. $p}
@{\lambda ${ident i} . $p}}}.
+*)
notation > "\exists list1 ident x sep , opt (: T). term 19 Px"
with precedence 20
@{ ${ fold right @{$Px} rec acc @{'exists (λ${ident x}.$acc)} } }
}.
+(* sigma ********************************************************************)
+
+notation < "hvbox(\Sigma ident i : ty break . p)"
+ left associative with precedence 20
+for @{'sigma (\lambda ${ident i} : $ty. $p) }.
+
+notation < "hvbox(\Sigma ident i break . p)"
+ with precedence 20
+for @{'sigma (\lambda ${ident i}. $p) }.
+
+(*
notation < "hvbox(\Sigma ident i opt (: ty) break . p)"
right associative with precedence 20
for @{ 'sigma ${default
@{\lambda ${ident i} : $ty. $p}
@{\lambda ${ident i} . $p}}}.
+*)
notation > "\Sigma list1 ident x sep , opt (: T). term 19 Px"
with precedence 20
@{ ${ fold right @{$Px} rec acc @{'sigma (λ${ident x}.$acc)} } }
}.
+(* other notations **********************************************************)
+
notation "hvbox(\langle term 19 a, break term 19 b\rangle)"
with precedence 90 for @{ 'pair $a $b}.