### Nuprl Lemma : baire-diff-from_wf

`∀[a:ℕ ⟶ ℕ]. ∀[k:ℕ].  (baire-diff-from(a;k) ∈ ℕ ⟶ ℕ)`

Proof

Definitions occuring in Statement :  baire-diff-from: `baire-diff-from(a;k)` nat: `ℕ` uall: `∀[x:A]. B[x]` member: `t ∈ T` function: `x:A ⟶ B[x]`
Definitions unfolded in proof :  assert: `↑b` bnot: `¬bb` sq_type: `SQType(T)` bfalse: `ff` top: `Top` exists: `∃x:A. B[x]` satisfiable_int_formula: `satisfiable_int_formula(fmla)` or: `P ∨ Q` decidable: `Dec(P)` ge: `i ≥ j ` guard: `{T}` prop: `ℙ` not: `¬A` false: `False` less_than': `less_than'(a;b)` le: `A ≤ B` subtype_rel: `A ⊆r B` uimplies: `b supposing a` and: `P ∧ Q` uiff: `uiff(P;Q)` ifthenelse: `if b then t else f fi ` btrue: `tt` it: `⋅` unit: `Unit` bool: `𝔹` implies: `P `` Q` all: `∀x:A. B[x]` nat: `ℕ` baire-diff-from: `baire-diff-from(a;k)` member: `t ∈ T` uall: `∀[x:A]. B[x]`
Lemmas referenced :  assert-bnot bool_subtype_base subtype_base_sq bool_cases_sqequal eqff_to_assert equal_wf int_formula_prop_wf int_formula_prop_eq_lemma int_term_value_add_lemma int_term_value_var_lemma int_term_value_constant_lemma int_formula_prop_le_lemma int_formula_prop_not_lemma int_formula_prop_and_lemma intformeq_wf itermAdd_wf itermVar_wf itermConstant_wf intformle_wf intformnot_wf intformand_wf satisfiable-full-omega-tt decidable__le nat_properties le_wf false_wf add_nat_wf nat-pred_wf nat_wf assert_of_le_int eqtt_to_assert bool_wf le_int_wf
Rules used in proof :  functionEquality axiomEquality cumulativity instantiate promote_hyp independent_functionElimination computeAll voidEquality voidElimination isect_memberEquality intEquality dependent_pairFormation dependent_functionElimination applyLambdaEquality equalitySymmetry equalityTransitivity independent_pairFormation natural_numberEquality addEquality dependent_set_memberEquality hypothesisEquality functionExtensionality applyEquality int_eqEquality independent_isectElimination productElimination equalityElimination unionElimination lambdaFormation hypothesis because_Cache rename setElimination thin isectElimination sqequalHypSubstitution extract_by_obid lambdaEquality sqequalRule cut introduction isect_memberFormation sqequalReflexivity computationStep sqequalTransitivity sqequalSubstitution

Latex:
\mforall{}[a:\mBbbN{}  {}\mrightarrow{}  \mBbbN{}].  \mforall{}[k:\mBbbN{}].    (baire-diff-from(a;k)  \mmember{}  \mBbbN{}  {}\mrightarrow{}  \mBbbN{})

Date html generated: 2017_04_21-AM-11_23_36
Last ObjectModification: 2017_04_20-PM-05_45_53

Theory : continuity

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