### Nuprl Lemma : filter2_wf

`∀[T:Type]. ∀[L:T List]. ∀[P:ℕ||L|| ⟶ 𝔹].  (filter2(P;L) ∈ T List)`

Proof

Definitions occuring in Statement :  filter2: `filter2(P;L)` length: `||as||` list: `T List` int_seg: `{i..j-}` bool: `𝔹` uall: `∀[x:A]. B[x]` member: `t ∈ T` function: `x:A ⟶ B[x]` natural_number: `\$n` universe: `Type`
Definitions unfolded in proof :  filter2: `filter2(P;L)` uall: `∀[x:A]. B[x]` member: `t ∈ T` nat: `ℕ` le: `A ≤ B` and: `P ∧ Q` less_than': `less_than'(a;b)` false: `False` not: `¬A` implies: `P `` Q` prop: `ℙ` int_seg: `{i..j-}` lelt: `i ≤ j < k` all: `∀x:A. B[x]` decidable: `Dec(P)` or: `P ∨ Q` less_than: `a < b` squash: `↓T` uiff: `uiff(P;Q)` uimplies: `b supposing a` satisfiable_int_formula: `satisfiable_int_formula(fmla)` exists: `∃x:A. B[x]` top: `Top` bool: `𝔹` unit: `Unit` it: `⋅` btrue: `tt` ifthenelse: `if b then t else f fi ` bfalse: `ff`
Lemmas referenced :  reduce2_wf list_wf nil_wf false_wf le_wf int_seg_wf length_wf decidable__lt add-is-int-iff satisfiable-full-omega-tt intformand_wf intformnot_wf intformless_wf itermVar_wf itermAdd_wf itermConstant_wf int_formula_prop_and_lemma int_formula_prop_not_lemma int_formula_prop_less_lemma int_term_value_var_lemma int_term_value_add_lemma int_term_value_constant_lemma int_formula_prop_wf lelt_wf bool_wf eqtt_to_assert cons_wf equal_wf
Rules used in proof :  sqequalSubstitution sqequalRule sqequalReflexivity sqequalTransitivity computationStep isect_memberFormation introduction cut extract_by_obid sqequalHypSubstitution isectElimination thin cumulativity hypothesisEquality hypothesis because_Cache dependent_set_memberEquality natural_numberEquality independent_pairFormation lambdaFormation lambdaEquality applyEquality functionExtensionality setElimination rename productElimination dependent_functionElimination unionElimination pointwiseFunctionality equalityTransitivity equalitySymmetry promote_hyp imageElimination baseClosed baseApply closedConclusion independent_isectElimination dependent_pairFormation int_eqEquality intEquality isect_memberEquality voidElimination voidEquality computeAll equalityElimination independent_functionElimination addEquality axiomEquality functionEquality universeEquality

Latex:
\mforall{}[T:Type].  \mforall{}[L:T  List].  \mforall{}[P:\mBbbN{}||L||  {}\mrightarrow{}  \mBbbB{}].    (filter2(P;L)  \mmember{}  T  List)

Date html generated: 2017_10_01-AM-08_35_05
Last ObjectModification: 2017_07_26-PM-04_25_41

Theory : list!

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