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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