+(* Bugged notation: $T is not used if provided *)
+notation > "\exists list1 ident x sep , opt (: T). term 19 Px"
+ with precedence 20
+ for ${ default
+ @{ ${ fold right @{$Px} rec acc @{'exists (λ${ident x}:$T.$acc)} } }
+ @{ ${ fold right @{$Px} rec acc @{'exists (λ${ident x}.$acc)} } }
+ }.
+
+notation "hvbox(\langle term 19 a, break term 19 b\rangle)"
+with precedence 90 for @{ 'pair $a $b}.
+
+notation "hvbox(x break \times y)" with precedence 70
+for @{ 'product $x $y}.
+
+notation < "\fst \nbsp term 90 x" with precedence 69 for @{'pi1a $x}.
+notation < "\snd \nbsp term 90 x" with precedence 69 for @{'pi2a $x}.
+
+notation < "\fst \nbsp term 90 x \nbsp term 90 y" with precedence 69 for @{'pi1b $x $y}.
+notation < "\snd \nbsp term 90 x \nbsp term 90 y" with precedence 69 for @{'pi2b $x $y}.
+
+notation > "\fst" with precedence 90 for @{'pi1}.
+notation > "\snd" with precedence 90 for @{'pi2}.