helm/software/matita/library/formal_topology/concrete_spaces.ma

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  14
  15 include "formal_topology/basic_pairs.ma".
  16
  17 interpretation "REL carrier" 'card c = (carrier c).
  18
  19 definition comprehension: ∀b:REL. (b → CProp) → Ω \sup |b| ≝
  20  λb:REL.λP.{x | ∃p: x ∈ b. P (mk_ssigma ?? x p)}.
  21
  22 interpretation "subset comprehension" 'comprehension s p =
  23  (comprehension s p).
  24
  25 definition ext: ∀o: basic_pair. (form o) → Ω \sup |(concr o)| ≝
  26  λo,f.{x ∈ (concr o) | x ♮(rel o) f}.
  27
  28 definition downarrow ≝
  29  λo: basic_pair.λa,b: form o.
  30   {c | ext ? c ⊆ ext ? a ∩ ext ? b }.