interpretation "powerset" 'powerset A = (powerset_setoid1 A).
interpretation "subset construction" 'subset \eta.x =
- (mk_powerset_carrier _ (mk_unary_morphism1 _ CPROP x _)).
+ (mk_powerset_carrier ? (mk_unary_morphism1 ? CPROP x ?)).
definition mem: ∀A. binary_morphism1 A (Ω \sup A) CPROP.
intros;
| apply s1; assumption]]
qed.
-interpretation "mem" 'mem a S = (fun21 ___ (mem _) a S).
+interpretation "mem" 'mem a S = (fun21 ??? (mem ?) a S).
definition subseteq: ∀A. binary_morphism1 (Ω \sup A) (Ω \sup A) CPROP.
intros;
apply (transitive_subseteq_operator ???? s s4) ]]
qed.
-interpretation "subseteq" 'subseteq U V = (fun21 ___ (subseteq _) U V).
+interpretation "subseteq" 'subseteq U V = (fun21 ??? (subseteq ?) U V).
| apply (. #‡e1); assumption]]
qed.
-interpretation "overlaps" 'overlaps U V = (fun21 ___ (overlaps _) U V).
+interpretation "overlaps" 'overlaps U V = (fun21 ??? (overlaps ?) U V).
definition intersects:
∀A. binary_morphism1 (Ω \sup A) (Ω \sup A) (Ω \sup A).
| apply (. (#‡e)‡(#‡e1)); assumption]]
qed.
-interpretation "intersects" 'intersects U V = (fun21 ___ (intersects _) U V).
+interpretation "intersects" 'intersects U V = (fun21 ??? (intersects ?) U V).
definition union:
∀A. binary_morphism1 (Ω \sup A) (Ω \sup A) (Ω \sup A).
| apply (. (#‡e)‡(#‡e1)); assumption]]
qed.
-interpretation "union" 'union U V = (fun21 ___ (union _) U V).
+interpretation "union" 'union U V = (fun21 ??? (union ?) U V).
(* qua non riesco a mettere set *)
definition singleton: ∀A:setoid. unary_morphism1 A (Ω \sup A).
intros; constructor 1;
- [ apply (λa:A.{b | eq ? a b}); unfold setoid1_of_setoid; simplify;
+ [ apply (λa:A.{b | a =_0 b}); unfold setoid1_of_setoid; simplify;
intros; simplify;
split; intro;
apply (.= e1);
[ apply a |4: apply a'] try assumption; apply sym; assumption]
qed.
-interpretation "singleton" 'singl a = (fun11 __ (singleton _) a).
+interpretation "singleton" 'singl a = (fun11 ?? (singleton ?) a).
definition big_intersects:
∀A:SET.∀I:SET.unary_morphism2 (setoid1_of_setoid I ⇒ Ω \sup A) (setoid2_of_setoid1 (Ω \sup A)).
intros; constructor 1;
[ intro; whd; whd in I;
- apply ({x | ∀i:I. x ∈ t i});
+ apply ({x | ∀i:I. x ∈ c i});
simplify; intros; split; intros; [ apply (. (e^-1‡#)); | apply (. e‡#); ]
apply f;
| intros; split; intros 2; simplify in f ⊢ %; intro;
∀A:SET.∀I:SET.unary_morphism2 (setoid1_of_setoid I ⇒ Ω \sup A) (setoid2_of_setoid1 (Ω \sup A)).
intros; constructor 1;
[ intro; whd; whd in A; whd in I;
- apply ({x | ∃i:carr I. x ∈ t i });
+ apply ({x | ∃i:I. x ∈ c i });
simplify; intros; split; intros; cases e1; clear e1; exists; [1,3:apply w]
[ apply (. (e^-1‡#)); | apply (. (e‡#)); ]
apply x;