### Nuprl Lemma : l_sum-wf-partial-nat

`∀[L:partial(ℕ) List]. (l_sum(L) ∈ partial(ℕ))`

Proof

Definitions occuring in Statement :  l_sum: `l_sum(L)` list: `T List` partial: `partial(T)` nat: `ℕ` uall: `∀[x:A]. B[x]` member: `t ∈ T`
Definitions unfolded in proof :  uall: `∀[x:A]. B[x]` member: `t ∈ T` all: `∀x:A. B[x]` nat: `ℕ` implies: `P `` Q` false: `False` ge: `i ≥ j ` uimplies: `b supposing a` not: `¬A` satisfiable_int_formula: `satisfiable_int_formula(fmla)` exists: `∃x:A. B[x]` top: `Top` and: `P ∧ Q` prop: `ℙ` or: `P ∨ Q` l_sum: `l_sum(L)` le: `A ≤ B` less_than': `less_than'(a;b)` cons: `[a / b]` decidable: `Dec(P)` colength: `colength(L)` nil: `[]` it: `⋅` guard: `{T}` so_lambda: `λ2x.t[x]` so_apply: `x[s]` sq_type: `SQType(T)` less_than: `a < b` squash: `↓T` so_lambda: `λ2x y.t[x; y]` so_apply: `x[s1;s2]` subtype_rel: `A ⊆r B`
Lemmas referenced :  nat_properties full-omega-unsat intformand_wf intformle_wf itermConstant_wf itermVar_wf intformless_wf istype-int int_formula_prop_and_lemma istype-void int_formula_prop_le_lemma int_term_value_constant_lemma int_term_value_var_lemma int_formula_prop_less_lemma int_formula_prop_wf ge_wf istype-less_than partial_wf nat_wf list-cases reduce_nil_lemma nat-partial-nat istype-false istype-le product_subtype_list colength-cons-not-zero istype-nat colength_wf_list decidable__le intformnot_wf int_formula_prop_not_lemma list_wf subtract-1-ge-0 subtype_base_sq intformeq_wf int_formula_prop_eq_lemma set_subtype_base int_subtype_base spread_cons_lemma decidable__equal_int subtract_wf itermSubtract_wf itermAdd_wf int_term_value_subtract_lemma int_term_value_add_lemma le_wf reduce_cons_lemma add-wf-partial-nat
Rules used in proof :  sqequalSubstitution sqequalTransitivity computationStep sqequalReflexivity Error :isect_memberFormation_alt,  introduction cut thin Error :lambdaFormation_alt,  extract_by_obid sqequalHypSubstitution isectElimination hypothesisEquality hypothesis setElimination rename sqequalRule intWeakElimination natural_numberEquality independent_isectElimination approximateComputation independent_functionElimination Error :dependent_pairFormation_alt,  Error :lambdaEquality_alt,  int_eqEquality dependent_functionElimination Error :isect_memberEquality_alt,  voidElimination independent_pairFormation Error :universeIsType,  axiomEquality equalityTransitivity equalitySymmetry Error :functionIsTypeImplies,  Error :inhabitedIsType,  unionElimination Error :dependent_set_memberEquality_alt,  promote_hyp hypothesis_subsumption productElimination Error :equalityIstype,  because_Cache instantiate applyLambdaEquality imageElimination baseApply closedConclusion baseClosed applyEquality intEquality sqequalBase

Latex:
\mforall{}[L:partial(\mBbbN{})  List].  (l\_sum(L)  \mmember{}  partial(\mBbbN{}))

Date html generated: 2019_06_20-PM-01_43_36
Last ObjectModification: 2019_02_21-PM-03_28_30

Theory : list_1

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