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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