matita/dama/constructive_connectives.ma

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  14
  15 set "baseuri" "cic:/matita/constructive_connectives/".
  16
  17 inductive or (A,B:Type) : Type \def
  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 ex (A:Type) (P:A→Prop) : Type \def
  25   ex_intro: ∀w:A. P w → ex A P.
  26
  27 notation < "hvbox(Σ ident i opt (: ty) break . p)"
  28   right associative with precedence 20
  29 for @{ 'sigma ${default
  30   @{\lambda ${ident i} : $ty. $p)}
  31   @{\lambda ${ident i} . $p}}}.
  32
  33 interpretation "constructive exists" 'sigma \eta.x =
  34   (cic:/matita/constructive_connectives/ex.ind#xpointer(1/1) _ x).
  35
  36 alias id "False" = "cic:/matita/logic/connectives/False.ind#xpointer(1/1)".
  37 definition Not ≝ λx:Type.False.
  38
  39 interpretation "constructive not" 'not x =
  40   (cic:/matita/constructive_connectives/Not.con x).