### Nuprl Lemma : cantor2baire-aux+1

`∀[a:ℕ ⟶ 𝔹]. ∀[n:ℕ].`
`  (cantor2baire-aux(a;n + 1) ~ if a (n + 1) then cantor2baire-aux(a;n) + 1 else cantor2baire-aux(a;n) fi )`

Proof

Definitions occuring in Statement :  cantor2baire-aux: `cantor2baire-aux(a;n)` nat: `ℕ` ifthenelse: `if b then t else f fi ` bool: `𝔹` uall: `∀[x:A]. B[x]` apply: `f a` function: `x:A ⟶ B[x]` add: `n + m` natural_number: `\$n` sqequal: `s ~ t`
Definitions unfolded in proof :  assert: `↑b` bnot: `¬bb` guard: `{T}` sq_type: `SQType(T)` or: `P ∨ Q` bfalse: `ff` prop: `ℙ` not: `¬A` false: `False` exists: `∃x:A. B[x]` satisfiable_int_formula: `satisfiable_int_formula(fmla)` ge: `i ≥ j ` 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]` top: `Top` nat: `ℕ` cantor2baire-aux: `cantor2baire-aux(a;n)` member: `t ∈ T` uall: `∀[x:A]. B[x]`
Lemmas referenced :  nat_wf neg_assert_of_eq_int assert-bnot bool_subtype_base subtype_base_sq bool_cases_sqequal equal_wf eqff_to_assert int_formula_prop_wf int_formula_prop_le_lemma int_term_value_constant_lemma int_term_value_var_lemma int_term_value_add_lemma int_formula_prop_eq_lemma int_formula_prop_and_lemma intformle_wf itermConstant_wf itermVar_wf itermAdd_wf intformeq_wf intformand_wf satisfiable-full-omega-tt nat_properties assert_of_eq_int eqtt_to_assert bool_wf eq_int_wf add-subtract-cancel primrec-unroll
Rules used in proof :  functionEquality sqequalAxiom independent_functionElimination cumulativity instantiate promote_hyp computeAll independent_pairFormation dependent_functionElimination intEquality int_eqEquality lambdaEquality dependent_pairFormation independent_isectElimination productElimination equalitySymmetry equalityTransitivity equalityElimination unionElimination lambdaFormation because_Cache voidEquality voidElimination isect_memberEquality natural_numberEquality hypothesis hypothesisEquality rename setElimination addEquality thin isectElimination sqequalHypSubstitution extract_by_obid sqequalRule cut introduction isect_memberFormation sqequalReflexivity computationStep sqequalTransitivity sqequalSubstitution

Latex:
\mforall{}[a:\mBbbN{}  {}\mrightarrow{}  \mBbbB{}].  \mforall{}[n:\mBbbN{}].
(cantor2baire-aux(a;n  +  1)  \msim{}  if  a  (n  +  1)
then  cantor2baire-aux(a;n)  +  1
else  cantor2baire-aux(a;n)
fi  )

Date html generated: 2017_04_21-AM-11_21_41
Last ObjectModification: 2017_04_20-PM-03_39_21

Theory : continuity

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