Nuprl Lemma : init0-cantor2baire
∀a:ℕ ⟶ 𝔹. init0(cantor2baire(a))
Proof
Definitions occuring in Statement :
init0: init0(a),
cantor2baire: cantor2baire(a),
nat: ℕ,
bool: 𝔹,
all: ∀x:A. B[x],
function: x:A ⟶ B[x]
Definitions unfolded in proof :
implies: P ⇒ Q,
not: ¬A,
less_than': less_than'(a;b),
and: P ∧ Q,
le: A ≤ B,
nat: ℕ,
false: False,
prop: ℙ,
exists: ∃x:A. B[x],
satisfiable_int_formula: satisfiable_int_formula(fmla),
uimplies: b supposing a,
uall: ∀[x:A]. B[x],
or: P ∨ Q,
decidable: Dec(P),
top: Top,
member: t ∈ T,
cantor2baire-aux: cantor2baire-aux(a;n),
init0: init0(a),
cantor2baire: cantor2baire(a),
all: ∀x:A. B[x]
Lemmas referenced :
bool_wf,
nat_wf,
le_wf,
false_wf,
int_formula_prop_wf,
int_term_value_constant_lemma,
int_formula_prop_eq_lemma,
int_formula_prop_not_lemma,
itermConstant_wf,
intformeq_wf,
intformnot_wf,
satisfiable-full-omega-tt,
decidable__equal_int,
primrec0_lemma
Rules used in proof :
functionEquality,
independent_pairFormation,
equalitySymmetry,
equalityTransitivity,
dependent_set_memberEquality,
computeAll,
hypothesisEquality,
intEquality,
lambdaEquality,
dependent_pairFormation,
independent_isectElimination,
isectElimination,
unionElimination,
because_Cache,
natural_numberEquality,
hypothesis,
voidEquality,
voidElimination,
isect_memberEquality,
thin,
dependent_functionElimination,
sqequalHypSubstitution,
extract_by_obid,
introduction,
cut,
sqequalRule,
lambdaFormation,
sqequalReflexivity,
computationStep,
sqequalTransitivity,
sqequalSubstitution
Latex:
\mforall{}a:\mBbbN{} {}\mrightarrow{} \mBbbB{}. init0(cantor2baire(a))
Date html generated:
2017_04_21-AM-11_22_27
Last ObjectModification:
2017_04_20-PM-04_24_21
Theory : continuity
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