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3 (*      ||M||                                                             *)
4 (*      ||A||       A project by Andrea Asperti                           *)
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11 (*        v         GNU General Public License Version 2                  *)
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14
15 set "baseuri" "cic:/matita/constructive_connectives/".
16
17 inductive Or (A,B:Type) : Type ≝
18    Left : A → Or A B
19  | Right : B → Or A B.
20
21 interpretation "constructive or" 'or x y =
22   (cic:/matita/constructive_connectives/Or.ind#xpointer(1/1) x y).
23
24 inductive And (A,B:Type) : Type ≝
25  | Conj : A → B → And A B.
26  
27 interpretation "constructive and" 'and x y =
28   (cic:/matita/constructive_connectives/And.ind#xpointer(1/1) x y).
29
30 inductive ex (A:Type) (P:A→Prop) : Type ≝
31   ex_intro: ∀w:A. P w → ex A P.
32
33 notation < "hvbox(Σ ident i opt (: ty) break . p)"
34   right associative with precedence 20
35 for @{ 'sigma ${default
36   @{\lambda ${ident i} : $ty. $p)}
37   @{\lambda ${ident i} . $p}}}.
38
39 interpretation "constructive exists" 'sigma \eta.x =
40   (cic:/matita/constructive_connectives/ex.ind#xpointer(1/1) _ x).
41
42 alias id "False" = "cic:/matita/logic/connectives/False.ind#xpointer(1/1)".
43 definition Not ≝ λx:Type.x → False.
44
45 interpretation "constructive not" 'not x = 
46   (cic:/matita/constructive_connectives/Not.con x).