Nuprl Lemma : countable-p-union_wf

∀[p:FinProbSpace]. ∀[A:ℕ ─→ p-open(p)].  (countable-p-union(i.A[i]) ∈ p-open(p))


Proof




Definitions occuring in Statement :  countable-p-union: countable-p-union(i.A[i]),  p-open: p-open(p),  finite-prob-space: FinProbSpace,  nat: ℕ,  uall: ∀[x:A]. B[x],  so_apply: x[s],  member: t ∈ T,  function: x:A ─→ B[x]
Lemmas :  assert_of_bnot,  eqff_to_assert,  iff_weakening_uiff,  iff_transitivity,  assert_of_eq_int,  eqtt_to_assert,  uiff_transitivity,  not_wf,  bnot_wf,  assert_wf,  equal-wf-T-base,  bool_wf,  eq_int_wf,  p-outcome_wf,  int_seg_wf,  nat_wf,  lelt_wf,  false_wf,  minus-zero,  minus-add,  add-commutes,  condition-implies-le,  le-add-cancel,  zero-add,  add-zero,  add-associates,  add_functionality_wrt_le,  not-equal-2,  decidable__lt,  length_upto,  iff_weakening_equal,  map_length_nat,  true_wf,  squash_wf,  less_than_wf,  upto_wf,  subtype_rel_self,  subtype_rel_dep_function,  le_wf,  all_wf,  int_seg_subtype-nat,  map_wf,  imax-list_wf,  imax-list-ub,  l_member_wf,  l_exists_iff,  member_upto,  subtype_rel_list,  member_map,  le-add-cancel2,  imax-list-lb,  less-iff-le,  sq_stable__le,  add-swap,  not-le-2,  decidable__le,  l_all_iff,  length_wf,  less_than_transitivity2,  decidable__equal_int,  int_subtype_base,  subtype_base_sq,  le_weakening,  le_weakening2,  member_upto2,  set_subtype_base,  equal_wf,  set_wf
\mforall{}[p:FinProbSpace].  \mforall{}[A:\mBbbN{}  {}\mrightarrow{}  p-open(p)].    (countable-p-union(i.A[i])  \mmember{}  p-open(p))



Date html generated: 2015_07_17-AM-08_00_43
Last ObjectModification: 2015_07_16-AM-09_51_59

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