### Nuprl Lemma : fibs_wf

`fibs() ∈ stream(ℕ)`

Proof

Definitions occuring in Statement :  fibs: `fibs()` stream: `stream(A)` nat: `ℕ` member: `t ∈ T`
Definitions unfolded in proof :  fibs: `fibs()` all: `∀x:A. B[x]` implies: `P `` Q` member: `t ∈ T` nat: `ℕ` uall: `∀[x:A]. B[x]` ge: `i ≥ j ` decidable: `Dec(P)` or: `P ∨ Q` uimplies: `b supposing a` not: `¬A` satisfiable_int_formula: `satisfiable_int_formula(fmla)` exists: `∃x:A. B[x]` false: `False` top: `Top` and: `P ∧ Q` prop: `ℙ` bool: `𝔹` unit: `Unit` it: `⋅` btrue: `tt` subtype_rel: `A ⊆r B` so_lambda: `λ2x.t[x]` so_apply: `x[s]` uiff: `uiff(P;Q)` ifthenelse: `if b then t else f fi ` bfalse: `ff` guard: `{T}` s-cons: `x.s` sq_type: `SQType(T)` iff: `P `⇐⇒` Q` rev_implies: `P `` Q` s-tl: `s-tl(s)` pi2: `snd(t)` bnot: `¬bb` assert: `↑b` nat_plus: `ℕ+` subtract: `n - m` less_than: `a < b` squash: `↓T` cand: `A c∧ B` stream: `stream(A)` corec: `corec(T.F[T])`
Lemmas referenced :  nat_properties decidable__le full-omega-unsat intformand_wf intformnot_wf intformle_wf itermConstant_wf itermAdd_wf itermVar_wf istype-int int_formula_prop_and_lemma istype-void int_formula_prop_not_lemma int_formula_prop_le_lemma int_term_value_constant_lemma int_term_value_add_lemma int_term_value_var_lemma int_formula_prop_wf istype-le istype-nat primrec-unroll lt_int_wf uiff_transitivity equal-wf-base bool_wf set_subtype_base le_wf int_subtype_base assert_wf less_than_wf eqtt_to_assert assert_of_lt_int le_int_wf bnot_wf eqff_to_assert assert_functionality_wrt_uiff bnot_of_lt_int assert_of_le_int intformless_wf int_formula_prop_less_lemma not_wf istype-less_than istype-assert bool_cases subtype_base_sq bool_subtype_base iff_transitivity iff_weakening_uiff assert_of_bnot nat_wf subtract_wf itermSubtract_wf int_term_value_subtract_lemma stream-zip_wf2 bool_cases_sqequal assert-bnot decidable__lt primrec1_lemma primrec0_lemma istype-top nat_plus_properties subtype_rel_wf primrec_wf top_wf istype-universe int_seg_wf primrec-wf-nat-plus add-subtract-cancel subtype_rel_product add-associates add-swap add-commutes zero-add ge_wf subtract-1-ge-0
Rules used in proof :  sqequalSubstitution sqequalTransitivity computationStep sqequalReflexivity sqequalRule cut Error :inhabitedIsType,  hypothesis Error :lambdaFormation_alt,  thin Error :equalityIstype,  hypothesisEquality sqequalHypSubstitution equalityTransitivity equalitySymmetry dependent_functionElimination independent_functionElimination Error :lambdaEquality_alt,  Error :dependent_set_memberEquality_alt,  addEquality setElimination rename introduction extract_by_obid isectElimination natural_numberEquality unionElimination independent_isectElimination approximateComputation Error :dependent_pairFormation_alt,  int_eqEquality Error :isect_memberEquality_alt,  voidElimination independent_pairFormation Error :universeIsType,  because_Cache equalityElimination baseApply closedConclusion baseClosed applyEquality intEquality productElimination independent_pairEquality Error :functionIsType,  instantiate cumulativity promote_hyp Error :productIsType,  universeEquality productEquality imageElimination intWeakElimination axiomEquality Error :functionIsTypeImplies

Latex:
fibs()  \mmember{}  stream(\mBbbN{})

Date html generated: 2019_06_20-PM-02_28_03
Last ObjectModification: 2019_03_13-PM-07_34_59

Theory : num_thy_1

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