### Nuprl Lemma : norm-list_wf_sq

`∀[T:Type]. (∀[N:sq-id-fun(T)]. (norm-list(N) ∈ sq-id-fun(T List))) supposing (value-type(T) and (T ⊆r Base))`

Proof

Definitions occuring in Statement :  norm-list: `norm-list(N)` list: `T List` sq-id-fun: `sq-id-fun(T)` value-type: `value-type(T)` uimplies: `b supposing a` subtype_rel: `A ⊆r B` uall: `∀[x:A]. B[x]` member: `t ∈ T` base: `Base` universe: `Type`
Definitions unfolded in proof :  uall: `∀[x:A]. B[x]` member: `t ∈ T` uimplies: `b supposing a` sq-id-fun: `sq-id-fun(T)` top: `Top` all: `∀x:A. B[x]` nat: `ℕ` implies: `P `` Q` false: `False` ge: `i ≥ j ` satisfiable_int_formula: `satisfiable_int_formula(fmla)` exists: `∃x:A. B[x]` not: `¬A` and: `P ∧ Q` prop: `ℙ` subtype_rel: `A ⊆r B` guard: `{T}` or: `P ∨ Q` norm-list: `norm-list(N)` so_lambda: `so_lambda(x,y,z.t[x; y; z])` so_apply: `x[s1;s2;s3]` cons: `[a / b]` colength: `colength(L)` so_lambda: `λ2x y.t[x; y]` so_apply: `x[s1;s2]` decidable: `Dec(P)` nil: `[]` it: `⋅` so_lambda: `λ2x.t[x]` so_apply: `x[s]` sq_type: `SQType(T)` less_than: `a < b` squash: `↓T` less_than': `less_than'(a;b)` has-value: `(a)↓` true: `True`
Lemmas referenced :  subtype_base_sq list_wf list_subtype_base top_wf sq-id-fun_wf value-type_wf subtype_rel_wf base_wf nat_properties satisfiable-full-omega-tt intformand_wf intformle_wf itermConstant_wf itermVar_wf intformless_wf int_formula_prop_and_lemma 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 less_than_wf equal-wf-T-base nat_wf colength_wf_list less_than_transitivity1 less_than_irreflexivity list-cases list_ind_nil_lemma nil_wf product_subtype_list spread_cons_lemma intformeq_wf itermAdd_wf int_formula_prop_eq_lemma int_term_value_add_lemma decidable__le intformnot_wf int_formula_prop_not_lemma le_wf equal_wf subtract_wf itermSubtract_wf int_term_value_subtract_lemma set_subtype_base int_subtype_base decidable__equal_int list_ind_cons_lemma value-type-has-value set-value-type sqequal-wf-base list-value-type cons_wf squash_wf true_wf
Rules used in proof :  sqequalSubstitution sqequalTransitivity computationStep sqequalReflexivity isect_memberFormation introduction cut extract_by_obid sqequalHypSubstitution isectElimination thin cumulativity hypothesisEquality hypothesis independent_isectElimination because_Cache functionExtensionality isect_memberEquality voidElimination voidEquality sqequalRule axiomEquality equalityTransitivity equalitySymmetry universeEquality lambdaFormation setElimination rename intWeakElimination natural_numberEquality dependent_pairFormation lambdaEquality int_eqEquality intEquality dependent_functionElimination independent_pairFormation computeAll independent_functionElimination applyEquality unionElimination dependent_set_memberEquality sqequalIntensionalEquality baseClosed promote_hyp hypothesis_subsumption productElimination applyLambdaEquality addEquality instantiate imageElimination callbyvalueReduce setEquality baseApply closedConclusion imageMemberEquality

Latex:
\mforall{}[T:Type]
(\mforall{}[N:sq-id-fun(T)].  (norm-list(N)  \mmember{}  sq-id-fun(T  List)))  supposing  (value-type(T)  and  (T  \msubseteq{}r  Base))

Date html generated: 2017_04_14-AM-09_27_51
Last ObjectModification: 2017_02_27-PM-04_01_19

Theory : list_1

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