### Nuprl Lemma : count_wf

`∀[A:Type]. ∀[P:A ⟶ 𝔹]. ∀[L:A List].  (count(P;L) ∈ ℕ)`

Proof

Definitions occuring in Statement :  count: `count(P;L)` list: `T List` nat: `ℕ` bool: `𝔹` uall: `∀[x:A]. B[x]` member: `t ∈ T` function: `x:A ⟶ B[x]` universe: `Type`
Definitions unfolded in proof :  uall: `∀[x:A]. B[x]` member: `t ∈ T` count: `count(P;L)` nat: `ℕ` all: `∀x:A. B[x]` implies: `P `` Q` bool: `𝔹` unit: `Unit` it: `⋅` btrue: `tt` uiff: `uiff(P;Q)` and: `P ∧ Q` uimplies: `b supposing a` ifthenelse: `if b then t else f fi ` ge: `i ≥ j ` decidable: `Dec(P)` or: `P ∨ Q` satisfiable_int_formula: `satisfiable_int_formula(fmla)` exists: `∃x:A. B[x]` false: `False` not: `¬A` top: `Top` prop: `ℙ` bfalse: `ff` sq_type: `SQType(T)` guard: `{T}` bnot: `¬bb` assert: `↑b` le: `A ≤ B` less_than': `less_than'(a;b)`
Lemmas referenced :  reduce_wf nat_wf ifthenelse_wf bool_wf eqtt_to_assert nat_properties decidable__le satisfiable-full-omega-tt intformand_wf intformnot_wf intformle_wf itermConstant_wf itermAdd_wf itermVar_wf int_formula_prop_and_lemma int_formula_prop_not_lemma int_formula_prop_le_lemma int_term_value_constant_lemma int_term_value_add_lemma int_term_value_var_lemma int_formula_prop_wf eqff_to_assert equal_wf bool_cases_sqequal subtype_base_sq bool_subtype_base assert-bnot le_wf false_wf list_wf
Rules used in proof :  sqequalSubstitution sqequalTransitivity computationStep sqequalReflexivity isect_memberFormation introduction cut sqequalRule extract_by_obid sqequalHypSubstitution isectElimination thin cumulativity hypothesisEquality hypothesis lambdaEquality dependent_set_memberEquality addEquality applyEquality functionExtensionality intEquality natural_numberEquality setElimination rename lambdaFormation unionElimination equalityElimination because_Cache productElimination independent_isectElimination dependent_functionElimination dependent_pairFormation int_eqEquality isect_memberEquality voidElimination voidEquality independent_pairFormation computeAll equalityTransitivity equalitySymmetry promote_hyp instantiate independent_functionElimination axiomEquality functionEquality universeEquality

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

Date html generated: 2017_04_14-AM-09_28_04
Last ObjectModification: 2017_02_27-PM-04_01_43

Theory : list_1

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