### Nuprl Lemma : l_sum_filter0

`∀[L:ℤ List]. (l_sum(L) = l_sum(filter(λx.(¬b(x =z 0));L)) ∈ ℤ)`

Proof

Definitions occuring in Statement :  l_sum: `l_sum(L)` filter: `filter(P;l)` list: `T List` bnot: `¬bb` eq_int: `(i =z j)` uall: `∀[x:A]. B[x]` lambda: `λx.A[x]` natural_number: `\$n` int: `ℤ` equal: `s = t ∈ T`
Definitions unfolded in proof :  l_sum: `l_sum(L)` uall: `∀[x:A]. B[x]` member: `t ∈ T` so_lambda: `λ2x.t[x]` subtype_rel: `A ⊆r B` uimplies: `b supposing a` so_apply: `x[s]` implies: `P `` Q` all: `∀x:A. B[x]` top: `Top` bool: `𝔹` unit: `Unit` it: `⋅` btrue: `tt` uiff: `uiff(P;Q)` and: `P ∧ Q` bnot: `¬bb` ifthenelse: `if b then t else f fi ` bfalse: `ff` decidable: `Dec(P)` or: `P ∨ Q` satisfiable_int_formula: `satisfiable_int_formula(fmla)` exists: `∃x:A. B[x]` false: `False` not: `¬A` prop: `ℙ` sq_type: `SQType(T)` guard: `{T}` assert: `↑b` nequal: `a ≠ b ∈ T `
Lemmas referenced :  list_induction equal-wf-base list_subtype_base int_subtype_base list_wf reduce_nil_lemma filter_nil_lemma reduce_cons_lemma filter_cons_lemma eq_int_wf bool_wf eqtt_to_assert assert_of_eq_int decidable__equal_int satisfiable-full-omega-tt intformand_wf intformnot_wf intformeq_wf itermAdd_wf itermVar_wf itermConstant_wf int_formula_prop_and_lemma int_formula_prop_not_lemma int_formula_prop_eq_lemma int_term_value_add_lemma int_term_value_var_lemma int_term_value_constant_lemma int_formula_prop_wf eqff_to_assert equal_wf bool_cases_sqequal subtype_base_sq bool_subtype_base assert-bnot neg_assert_of_eq_int
Rules used in proof :  sqequalSubstitution sqequalRule sqequalReflexivity sqequalTransitivity computationStep isect_memberFormation cut thin introduction extract_by_obid sqequalHypSubstitution isectElimination intEquality lambdaEquality baseApply closedConclusion baseClosed hypothesisEquality applyEquality because_Cache independent_isectElimination hypothesis independent_functionElimination dependent_functionElimination isect_memberEquality voidElimination voidEquality natural_numberEquality lambdaFormation rename unionElimination equalityElimination productElimination equalityTransitivity equalitySymmetry dependent_pairFormation int_eqEquality independent_pairFormation computeAll promote_hyp instantiate cumulativity

Latex:
\mforall{}[L:\mBbbZ{}  List].  (l\_sum(L)  =  l\_sum(filter(\mlambda{}x.(\mneg{}\msubb{}(x  =\msubz{}  0));L)))

Date html generated: 2017_04_17-AM-08_38_13
Last ObjectModification: 2017_02_27-PM-04_58_02

Theory : list_1

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