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4 (* ||A|| A project by Andrea Asperti *)
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7 (* ||T|| The HELM team. *)
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15 include "Class/defs.ma".
17 (* QUANTIFICATION DOMAINS
18 - These are the categories on which we allow quantification.
19 - We set up single quantifiers, parametric on the domain.
22 record Domain: Type ≝ {
26 (* internal universal quantification *)
27 inductive dall (D:Domain) (P:D → Prop): Prop ≝
28 | dall_intro: (∀d. cin ? d → P d) → dall D P
31 interpretation "internal for all" 'iforall η.x = (dall ? x).
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
38 interpretation "internal exists" 'iexists η.x = (dex ? x).