### Nuprl Lemma : enum-fin-seq_wf

`∀[m:ℕ]. (enum-fin-seq(m) ∈ ℕ ⟶ 𝔹 List(2^m))`

Proof

Definitions occuring in Statement :  enum-fin-seq: `enum-fin-seq(m)` exp: `i^n` list_n: `A List(n)` nat: `ℕ` bool: `𝔹` uall: `∀[x:A]. B[x]` member: `t ∈ T` function: `x:A ⟶ B[x]` natural_number: `\$n`
Definitions unfolded in proof :  uall: `∀[x:A]. B[x]` member: `t ∈ T` list_n: `A List(n)` prop: `ℙ` enum-fin-seq: `enum-fin-seq(m)` nat: `ℕ` int_seg: `{i..j-}` false: `False` implies: `P `` Q` not: `¬A` ge: `i ≥ j ` uimplies: `b supposing a` satisfiable_int_formula: `satisfiable_int_formula(fmla)` exists: `∃x:A. B[x]` all: `∀x:A. B[x]` top: `Top` and: `P ∧ Q` decidable: `Dec(P)` or: `P ∨ Q` bool: `𝔹` unit: `Unit` it: `⋅` btrue: `tt` uiff: `uiff(P;Q)` ifthenelse: `if b then t else f fi ` bfalse: `ff` sq_type: `SQType(T)` guard: `{T}` bnot: `¬bb` assert: `↑b` nat_plus: `ℕ+` squash: `↓T` true: `True` subtype_rel: `A ⊆r B` iff: `P `⇐⇒` Q` rev_implies: `P `` Q`
Lemmas referenced :  equal_wf length_wf nat_wf bool_wf exp_wf2 primrec_wf list_wf cons_wf btrue_wf nil_wf append_wf map_wf bfalse_wf int_seg_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 exp0_lemma decidable__le subtract_wf intformnot_wf itermSubtract_wf int_formula_prop_not_lemma int_term_value_subtract_lemma primrec0_lemma length_of_cons_lemma length_of_nil_lemma primrec-unroll eq_int_wf eqtt_to_assert assert_of_eq_int intformeq_wf int_formula_prop_eq_lemma eqff_to_assert bool_cases_sqequal subtype_base_sq bool_subtype_base assert-bnot neg_assert_of_eq_int length-append map-length two-mul exp_step squash_wf true_wf iff_weakening_equal
Rules used in proof :  sqequalSubstitution sqequalTransitivity computationStep sqequalReflexivity isect_memberFormation introduction cut dependent_set_memberEquality extract_by_obid sqequalHypSubstitution isectElimination thin intEquality functionEquality hypothesis hypothesisEquality natural_numberEquality sqequalRule axiomEquality equalityTransitivity equalitySymmetry because_Cache lambdaEquality int_eqEquality setElimination rename applyEquality functionExtensionality intWeakElimination lambdaFormation independent_isectElimination dependent_pairFormation dependent_functionElimination isect_memberEquality voidElimination voidEquality independent_pairFormation computeAll independent_functionElimination unionElimination equalityElimination productElimination promote_hyp instantiate cumulativity imageElimination universeEquality multiplyEquality imageMemberEquality baseClosed

Latex:
\mforall{}[m:\mBbbN{}].  (enum-fin-seq(m)  \mmember{}  \mBbbN{}  {}\mrightarrow{}  \mBbbB{}  List(2\^{}m))

Date html generated: 2017_04_20-AM-07_22_34
Last ObjectModification: 2017_02_27-PM-05_58_24

Theory : continuity

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