### Nuprl Lemma : increasing-baire-diff-from

`∀a:ℕ ⟶ ℕ. ∀n:ℕ.  (increasing-sequence(a) `` increasing-sequence(baire-diff-from(a;n)))`

Proof

Definitions occuring in Statement :  baire-diff-from: `baire-diff-from(a;k)` increasing-sequence: `increasing-sequence(a)` nat: `ℕ` all: `∀x:A. B[x]` implies: `P `` Q` function: `x:A ⟶ B[x]`
Definitions unfolded in proof :  less_than': `less_than'(a;b)` le: `A ≤ B` nat-pred: `n-1` so_apply: `x[s]` so_lambda: `λ2x.t[x]` nequal: `a ≠ b ∈ T ` assert: `↑b` bnot: `¬bb` sq_type: `SQType(T)` bfalse: `ff` guard: `{T}` prop: `ℙ` top: `Top` not: `¬A` false: `False` exists: `∃x:A. B[x]` satisfiable_int_formula: `satisfiable_int_formula(fmla)` decidable: `Dec(P)` ge: `i ≥ j ` or: `P ∨ Q` subtype_rel: `A ⊆r B` ifthenelse: `if b then t else f fi ` uimplies: `b supposing a` and: `P ∧ Q` uiff: `uiff(P;Q)` btrue: `tt` it: `⋅` unit: `Unit` bool: `𝔹` nat: `ℕ` uall: `∀[x:A]. B[x]` member: `t ∈ T` baire-diff-from: `baire-diff-from(a;k)` increasing-sequence: `increasing-sequence(a)` implies: `P `` Q` all: `∀x:A. B[x]`
Lemmas referenced :  false_wf subtract_wf add_nat_wf add-subtract-cancel int_subtype_base set_subtype_base increasing-sequence_wf neg_assert_of_eq_int assert-bnot bool_subtype_base subtype_base_sq bool_cases_sqequal eqff_to_assert equal_wf le_wf int_formula_prop_le_lemma int_formula_prop_and_lemma intformle_wf intformand_wf decidable__le int_formula_prop_wf decidable__equal_int int_term_value_constant_lemma int_term_value_var_lemma int_term_value_add_lemma int_formula_prop_eq_lemma int_formula_prop_not_lemma itermConstant_wf itermVar_wf itermAdd_wf intformeq_wf intformnot_wf satisfiable-full-omega-tt decidable__equal_nat nat_properties assert_of_eq_int nat-pred_wf nat_wf eq_int_wf assert_of_le_int eqtt_to_assert bool_wf le_int_wf
Rules used in proof :  inrFormation functionEquality cumulativity int_eqReduceFalseSq instantiate promote_hyp independent_pairFormation applyLambdaEquality dependent_set_memberEquality computeAll independent_functionElimination voidEquality voidElimination isect_memberEquality intEquality int_eqEquality lambdaEquality dependent_pairFormation dependent_functionElimination inlFormation int_eqReduceTrueSq because_Cache functionExtensionality applyEquality independent_isectElimination productElimination equalitySymmetry equalityTransitivity equalityElimination unionElimination natural_numberEquality addEquality hypothesis hypothesisEquality rename setElimination thin isectElimination sqequalHypSubstitution extract_by_obid introduction cut sqequalRule lambdaFormation sqequalReflexivity computationStep sqequalTransitivity sqequalSubstitution

Latex:
\mforall{}a:\mBbbN{}  {}\mrightarrow{}  \mBbbN{}.  \mforall{}n:\mBbbN{}.    (increasing-sequence(a)  {}\mRightarrow{}  increasing-sequence(baire-diff-from(a;n)))

Date html generated: 2017_04_21-AM-11_23_56
Last ObjectModification: 2017_04_20-PM-05_55_47

Theory : continuity

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