Nuprl Lemma : cantor2baire-is-increasing
∀a:ℕ ⟶ 𝔹. increasing-sequence(cantor2baire(a))
Proof
Definitions occuring in Statement :
cantor2baire: cantor2baire(a),
increasing-sequence: increasing-sequence(a),
nat: ℕ,
bool: 𝔹,
all: ∀x:A. B[x],
function: x:A ⟶ B[x]
Definitions unfolded in proof :
assert: ↑b,
bnot: ¬bb,
sq_type: SQType(T),
bfalse: ff,
less_than': less_than'(a;b),
le: A ≤ B,
subtype_rel: A ⊆r B,
guard: {T},
ifthenelse: if b then t else f fi ,
uiff: uiff(P;Q),
btrue: tt,
it: ⋅,
unit: Unit,
bool: 𝔹,
prop: ℙ,
and: P ∧ Q,
top: Top,
not: ¬A,
implies: P ⇒ Q,
false: False,
exists: ∃x:A. B[x],
satisfiable_int_formula: satisfiable_int_formula(fmla),
uimplies: b supposing a,
or: P ∨ Q,
decidable: Dec(P),
ge: i ≥ j ,
uall: ∀[x:A]. B[x],
nat: ℕ,
member: t ∈ T,
cantor2baire: cantor2baire(a),
increasing-sequence: increasing-sequence(a),
all: ∀x:A. B[x]
Lemmas referenced :
cantor2baire-aux+1,
assert-bnot,
bool_subtype_base,
subtype_base_sq,
bool_cases_sqequal,
eqff_to_assert,
equal_wf,
add-is-int-iff,
false_wf,
add_nat_wf,
int_formula_prop_eq_lemma,
intformeq_wf,
cantor2baire-aux_wf,
decidable__equal_int,
eqtt_to_assert,
le_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,
nat_properties,
bool_wf,
nat_wf
Rules used in proof :
inlFormation,
cumulativity,
instantiate,
independent_functionElimination,
baseClosed,
closedConclusion,
baseApply,
promote_hyp,
pointwiseFunctionality,
applyLambdaEquality,
equalitySymmetry,
equalityTransitivity,
inrFormation,
productElimination,
because_Cache,
equalityElimination,
computeAll,
independent_pairFormation,
voidEquality,
voidElimination,
isect_memberEquality,
intEquality,
int_eqEquality,
lambdaEquality,
dependent_pairFormation,
independent_isectElimination,
unionElimination,
dependent_functionElimination,
isectElimination,
natural_numberEquality,
rename,
thin,
setElimination,
sqequalHypSubstitution,
addEquality,
dependent_set_memberEquality,
functionExtensionality,
applyEquality,
hypothesisEquality,
functionEquality,
hypothesis,
extract_by_obid,
introduction,
cut,
sqequalRule,
lambdaFormation,
sqequalReflexivity,
computationStep,
sqequalTransitivity,
sqequalSubstitution
Latex:
\mforall{}a:\mBbbN{} {}\mrightarrow{} \mBbbB{}. increasing-sequence(cantor2baire(a))
Date html generated:
2017_04_21-AM-11_21_59
Last ObjectModification:
2017_04_20-PM-03_40_11
Theory : continuity
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