helm/software/matita/contribs/limits/Domain/defs.ma

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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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  13 (**************************************************************************)
  14
  15 include "Class/defs.ma".
  16
  17 (* QUANTIFICATION DOMAINS
  18    - These are the categories on which we allow quantification.
  19    - We set up single quantifiers, parametric on the domain.
  20 *)
  21
  22 record Domain: Type ≝ {
  23    domain:> Class
  24 }.
  25
  26 (* internal universal quantification *)
  27 inductive dall (D:Domain) (P:D → Prop): Prop ≝
  28    | dall_intro: (∀d. cin ? d → P d) → dall D P
  29 .
  30
  31 interpretation "internal for all" 'iforall η.x = (dall ? x).
  32
  33 (* internal existential quantification *)
  34 inductive dex (D:Domain) (P:D → Prop): Prop ≝
  35    | dex_intro: ∀d. cin D d → P d → dex D P
  36 .
  37
  38 interpretation "internal exists" 'iexists η.x = (dex ? x).