domain structure. This makes domains easier to use
*)
-
-
record Domain: Type \def {
- qd: Class
+ qd:> Class
}.
-coercion qd.
-
+(* internal universal quantification *)
+inductive dall (D:Domain) (P:D \to Prop) : Prop \def
+ | dall_intro: (\forall d:D. cin D d \to P d) \to dall D P.
+(* internal existential quantification *)
+inductive dex (D:Domain) (P:D \to Prop) : Prop \def
+ | dex_intro: \forall d:D. cin D d \land P d \to dex D P.
-(* internal universal quantification *)
-inductive iall (D:Domain) (P:D \to Prop) : Prop \def
- | iall_intro: (\forall d:D. cin D d \to P d) \to iall D P.
+(* notations **************************************************************)
(*CSC: the URI must disappear: there is a bug now *)
-interpretation "internal for all" 'iall \eta.x =
- (cic:/matita/PREDICATIVE-TOPOLOGY/domain_defs/iall.ind#xpointer(1/1) _ x).
+interpretation "internal for all" 'iforall \eta.x =
+ (cic:/matita/PREDICATIVE-TOPOLOGY/domain_defs/dall.ind#xpointer(1/1) _ x).
-notation < "hvbox(\iall ident i opt (: ty) break . p)"
+notation > "hvbox(\iforall ident i opt (: ty) break . p)"
right associative with precedence 20
-for @{ 'iall ${default
+for @{ 'iforall ${default
@{\lambda ${ident i} : $ty. $p)}
@{\lambda ${ident i} . $p}}}.
-
-
-(* internal existential quantification *)
-inductive iex (D:Domain) (P:D \to Prop) : Prop \def
- | iex_intro: \forall d:D. cin D d \land P d \to iex D P.
-
(*CSC: the URI must disappear: there is a bug now *)
-interpretation "internal exist" 'iexist \eta.x =
- (cic:/matita/PREDICATIVE-TOPOLOGY/domain_defs/iex.ind#xpointer(1/1) _ x).
+interpretation "internal exists" 'dexists \eta.x =
+ (cic:/matita/PREDICATIVE-TOPOLOGY/domain_defs/dex.ind#xpointer(1/1) _ x).
-notation < "hvbox(\iexist ident i opt (: ty) break . p)"
+notation > "hvbox(\iexists ident i opt (: ty) break . p)"
right associative with precedence 20
-for @{ 'iexist ${default
+for @{ 'dexists ${default
@{\lambda ${ident i} : $ty. $p)}
@{\lambda ${ident i} . $p}}}.