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

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

Proof

Definitions occuring in Statement :  baire-diff-from: `baire-diff-from(a;k)` nat: `ℕ` all: `∀x:A. B[x]` not: `¬A` apply: `f a` function: `x:A ⟶ B[x]` equal: `s = t ∈ T`
Definitions unfolded in proof :  int_upper: `{i...}` nequal: `a ≠ b ∈ T ` assert: `↑b` bnot: `¬bb` rev_implies: `P `` Q` iff: `P `⇐⇒` Q` true: `True` squash: `↓T` sq_type: `SQType(T)` bfalse: `ff` or: `P ∨ Q` decidable: `Dec(P)` top: `Top` exists: `∃x:A. B[x]` satisfiable_int_formula: `satisfiable_int_formula(fmla)` ge: `i ≥ j ` guard: `{T}` subtype_rel: `A ⊆r B` prop: `ℙ` not: `¬A` false: `False` less_than': `less_than'(a;b)` le: `A ≤ B` nat-pred: `n-1` 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` nat: `ℕ` uall: `∀[x:A]. B[x]` member: `t ∈ T` baire-diff-from: `baire-diff-from(a;k)` all: `∀x:A. B[x]`
Lemmas referenced :  add_nat_wf int_term_value_subtract_lemma itermSubtract_wf int_upper_properties subtract_wf zero-add nequal-le-implies false_wf int_upper_subtype_nat not_assert_elim neg_assert_of_eq_int assert-bnot bool_subtype_base bool_cases_sqequal btrue_neq_bfalse assert_elim bnot_wf bfalse_wf and_wf iff_weakening_equal btrue_wf eq_int_eq_true int_subtype_base subtype_base_sq eqff_to_assert int_formula_prop_not_lemma int_formula_prop_le_lemma intformnot_wf intformle_wf decidable__le equal_wf int_formula_prop_wf int_term_value_constant_lemma int_term_value_add_lemma int_term_value_var_lemma int_formula_prop_eq_lemma int_formula_prop_and_lemma itermConstant_wf itermAdd_wf itermVar_wf intformeq_wf intformand_wf satisfiable-full-omega-tt nat_properties nat_wf le_wf assert_of_eq_int eq_int_wf assert_of_le_int eqtt_to_assert bool_wf le_int_wf
Rules used in proof :  functionEquality hypothesis_subsumption int_eqReduceFalseSq promote_hyp universeEquality baseClosed imageMemberEquality imageElimination independent_functionElimination cumulativity instantiate addEquality computeAll voidEquality voidElimination isect_memberEquality dependent_functionElimination intEquality int_eqEquality lambdaEquality dependent_pairFormation applyLambdaEquality functionExtensionality independent_pairFormation dependent_set_memberEquality applyEquality int_eqReduceTrueSq natural_numberEquality independent_isectElimination productElimination equalitySymmetry equalityTransitivity equalityElimination unionElimination because_Cache 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{}.    (\mneg{}((a  n)  =  (baire-diff-from(a;n)  n)))

Date html generated: 2017_04_21-AM-11_24_10
Last ObjectModification: 2017_04_20-PM-06_29_52

Theory : continuity

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