set "baseuri" "cic:/matita/constructive_connectives/".
-inductive or (A,B:Type) : Type \def
- Left : A → or A B
- | Right : B → or A B.
+inductive Or (A,B:Type) : Type ≝
+ Left : A → Or A B
+ | Right : B → Or A B.
-interpretation "classical or" 'or x y =
- (cic:/matita/constructive_connectives/or.ind#xpointer(1/1) x y).
+interpretation "constructive or" 'or x y =
+ (cic:/matita/constructive_connectives/Or.ind#xpointer(1/1) x y).
+inductive And (A,B:Type) : Type ≝
+ | Conj : A → B → And A B.
+
+interpretation "constructive and" 'and x y =
+ (cic:/matita/constructive_connectives/And.ind#xpointer(1/1) x y).
+
+inductive ex (A:Type) (P:A→Prop) : Type ≝
+ ex_intro: ∀w:A. P w → ex A P.
+
+notation < "hvbox(Σ ident i opt (: ty) break . p)"
+ right associative with precedence 20
+for @{ 'sigma ${default
+ @{\lambda ${ident i} : $ty. $p)}
+ @{\lambda ${ident i} . $p}}}.
+
+interpretation "constructive exists" 'sigma \eta.x =
+ (cic:/matita/constructive_connectives/ex.ind#xpointer(1/1) _ x).
+
+alias id "False" = "cic:/matita/logic/connectives/False.ind#xpointer(1/1)".
+definition Not ≝ λx:Type.x → False.
+
+interpretation "constructive not" 'not x =
+ (cic:/matita/constructive_connectives/Not.con x).
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