Nuprl Lemma : cantor2baire_wf
∀[a:ℕ ⟶ 𝔹]. (cantor2baire(a) ∈ ℕ ⟶ ℕ)
Proof
Definitions occuring in Statement :
cantor2baire: cantor2baire(a),
nat: ℕ,
bool: 𝔹,
uall: ∀[x:A]. B[x],
member: t ∈ T,
function: x:A ⟶ B[x]
Definitions unfolded in proof :
bfalse: ff,
top: Top,
exists: ∃x:A. B[x],
satisfiable_int_formula: satisfiable_int_formula(fmla),
or: P ∨ Q,
decidable: Dec(P),
lelt: i ≤ j < k,
ge: i ≥ j ,
int_seg: {i..j-},
guard: {T},
uiff: uiff(P;Q),
ifthenelse: if b then t else f fi ,
btrue: tt,
it: ⋅,
unit: Unit,
bool: 𝔹,
all: ∀x:A. B[x],
uimplies: b supposing a,
subtype_rel: A ⊆r B,
prop: ℙ,
implies: P ⇒ Q,
not: ¬A,
false: False,
less_than': less_than'(a;b),
and: P ∧ Q,
le: A ≤ B,
nat: ℕ,
cantor2baire: cantor2baire(a),
member: t ∈ T,
uall: ∀[x:A]. B[x]
Lemmas referenced :
int_seg_wf,
equal_wf,
int_formula_prop_wf,
int_term_value_var_lemma,
int_term_value_add_lemma,
int_term_value_constant_lemma,
int_formula_prop_le_lemma,
int_formula_prop_not_lemma,
int_formula_prop_and_lemma,
itermVar_wf,
itermAdd_wf,
itermConstant_wf,
intformle_wf,
intformnot_wf,
intformand_wf,
satisfiable-full-omega-tt,
decidable__le,
int_seg_properties,
nat_properties,
eqtt_to_assert,
bool_wf,
int_seg_subtype_nat,
le_wf,
false_wf,
nat_wf,
primrec_wf
Rules used in proof :
functionEquality,
axiomEquality,
independent_functionElimination,
equalitySymmetry,
equalityTransitivity,
computeAll,
voidEquality,
voidElimination,
isect_memberEquality,
intEquality,
int_eqEquality,
dependent_pairFormation,
dependent_functionElimination,
addEquality,
productElimination,
equalityElimination,
unionElimination,
independent_isectElimination,
rename,
setElimination,
because_Cache,
functionExtensionality,
applyEquality,
lambdaFormation,
independent_pairFormation,
natural_numberEquality,
dependent_set_memberEquality,
hypothesisEquality,
hypothesis,
thin,
isectElimination,
sqequalHypSubstitution,
extract_by_obid,
lambdaEquality,
sqequalRule,
cut,
introduction,
isect_memberFormation,
sqequalReflexivity,
computationStep,
sqequalTransitivity,
sqequalSubstitution
Latex:
\mforall{}[a:\mBbbN{} {}\mrightarrow{} \mBbbB{}]. (cantor2baire(a) \mmember{} \mBbbN{} {}\mrightarrow{} \mBbbN{})
Date html generated:
2017_04_20-AM-07_38_07
Last ObjectModification:
2017_04_19-PM-03_35_45
Theory : continuity
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