### Nuprl Lemma : eq-upto-baire-diff-from

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

Proof

Definitions occuring in Statement :  baire-diff-from: `baire-diff-from(a;k)` int_seg: `{i..j-}` nat: `ℕ` uall: `∀[x:A]. B[x]` function: `x:A ⟶ B[x]` natural_number: `\$n` equal: `s = t ∈ T`
Definitions unfolded in proof :  less_than': `less_than'(a;b)` le: `A ≤ B` assert: `↑b` bnot: `¬bb` sq_type: `SQType(T)` bfalse: `ff` or: `P ∨ Q` decidable: `Dec(P)` subtype_rel: `A ⊆r B` prop: `ℙ` top: `Top` not: `¬A` false: `False` exists: `∃x:A. B[x]` satisfiable_int_formula: `satisfiable_int_formula(fmla)` lelt: `i ≤ j < k` ge: `i ≥ j ` guard: `{T}` 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` implies: `P `` Q` all: `∀x:A. B[x]` int_seg: `{i..j-}` nat: `ℕ` baire-diff-from: `baire-diff-from(a;k)` member: `t ∈ T` uall: `∀[x:A]. B[x]`
Lemmas referenced :  int_seg_wf false_wf int_seg_subtype_nat assert-bnot bool_subtype_base subtype_base_sq bool_cases_sqequal equal_wf eqff_to_assert le_wf nat-pred_wf int_formula_prop_wf int_formula_prop_less_lemma int_term_value_var_lemma int_formula_prop_le_lemma int_formula_prop_and_lemma intformless_wf itermVar_wf intformle_wf intformand_wf satisfiable-full-omega-tt nat_wf decidable__equal_int nat_properties int_seg_properties assert_of_le_int eqtt_to_assert bool_wf le_int_wf
Rules used in proof :  functionEquality axiomEquality independent_functionElimination cumulativity instantiate promote_hyp dependent_set_memberEquality addEquality computeAll independent_pairFormation voidEquality voidElimination isect_memberEquality intEquality int_eqEquality lambdaEquality dependent_pairFormation applyEquality dependent_functionElimination natural_numberEquality because_Cache independent_isectElimination productElimination equalitySymmetry equalityTransitivity equalityElimination unionElimination lambdaFormation hypothesis hypothesisEquality rename setElimination thin isectElimination sqequalHypSubstitution extract_by_obid sqequalRule functionExtensionality cut introduction isect_memberFormation sqequalReflexivity computationStep sqequalTransitivity sqequalSubstitution

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

Date html generated: 2017_04_21-AM-11_23_43
Last ObjectModification: 2017_04_20-PM-05_47_19

Theory : continuity

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