### Nuprl Lemma : list-at_wf

`∀[T:Type]. ∀[ns:colist(ℕ)]. ∀[L:colist(T)].  (L@ns ∈ colist(T))`

Proof

Definitions occuring in Statement :  list-at: `L1@L2` colist: `colist(T)` nat: `ℕ` uall: `∀[x:A]. B[x]` member: `t ∈ T` universe: `Type`
Definitions unfolded in proof :  b-union: `A ⋃ B` tunion: `⋃x:A.B[x]` decidable: `Dec(P)` pi2: `snd(t)` list-at: `L1@L2` ext-eq: `A ≡ B` subtype_rel: `A ⊆r B` nil: `[]` cons: `[a / b]` bool: `𝔹` unit: `Unit` it: `⋅` btrue: `tt` uiff: `uiff(P;Q)` bfalse: `ff` or: `P ∨ Q` sq_type: `SQType(T)` guard: `{T}` bnot: `¬bb` ifthenelse: `if b then t else f fi ` assert: `↑b` rev_implies: `P `` Q` iff: `P `⇐⇒` Q` uall: `∀[x:A]. B[x]` member: `t ∈ T` colist: `colist(T)` corec: `corec(T.F[T])` 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]` all: `∀x:A. B[x]` top: `Top` and: `P ∧ Q` prop: `ℙ`
Lemmas referenced :  intformeq_wf int_formula_prop_eq_lemma bfalse_wf null_cons_lemma reduce_hd_cons_lemma reduce_tl_cons_lemma btrue_wf it_wf ifthenelse_wf primrec_wf subtract_wf decidable__le intformnot_wf itermSubtract_wf int_formula_prop_not_lemma int_term_value_subtract_lemma istype-le top_wf b-union_wf int_seg_wf null_nil_lemma reduce_tl_nil_lemma colist-ext isaxiom_wf_listunion subtype_rel_b-union-left unit_wf2 axiom-listunion subtype_rel_b-union-right non-axiom-listunion primrec-unroll lt_int_wf eqtt_to_assert assert_of_lt_int eqff_to_assert bool_cases_sqequal subtype_base_sq bool_wf bool_subtype_base assert-bnot iff_weakening_uiff assert_wf less_than_wf primrec0_lemma 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 colist_wf subtract-1-ge-0 istype-nat nat_wf istype-universe
Rules used in proof :  int_eqReduceFalseSq independent_pairEquality imageMemberEquality Error :dependent_pairEquality_alt,  closedConclusion Error :dependent_set_memberEquality_alt,  baseClosed hypothesis_subsumption applyEquality productEquality unionElimination equalityElimination productElimination Error :equalityIstype,  promote_hyp cumulativity sqequalSubstitution sqequalTransitivity computationStep sqequalReflexivity Error :isect_memberFormation_alt,  introduction cut Error :isect_memberEquality_alt,  thin extract_by_obid sqequalHypSubstitution isectElimination hypothesisEquality hypothesis setElimination rename sqequalRule intWeakElimination Error :lambdaFormation_alt,  natural_numberEquality independent_isectElimination approximateComputation independent_functionElimination Error :dependent_pairFormation_alt,  Error :lambdaEquality_alt,  int_eqEquality dependent_functionElimination voidElimination independent_pairFormation Error :universeIsType,  axiomEquality equalityTransitivity equalitySymmetry Error :functionIsTypeImplies,  Error :inhabitedIsType,  because_Cache Error :isectIsTypeImplies,  instantiate universeEquality

Latex:
\mforall{}[T:Type].  \mforall{}[ns:colist(\mBbbN{})].  \mforall{}[L:colist(T)].    (L@ns  \mmember{}  colist(T))

Date html generated: 2019_06_20-PM-02_12_44
Last ObjectModification: 2019_06_20-PM-02_08_42

Theory : list_1

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