Nuprl Lemma : init0-baire-eq-from
∀a:ℕ ⟶ ℕ. ∀n:ℕ.  (init0(a) 
⇒ init0(baire_eq_from(a;n)))
Proof
Definitions occuring in Statement : 
baire_eq_from: baire_eq_from(a;k)
, 
init0: init0(a)
, 
nat: ℕ
, 
all: ∀x:A. B[x]
, 
implies: P 
⇒ Q
, 
function: x:A ⟶ B[x]
Definitions unfolded in proof : 
so_apply: x[s]
, 
so_lambda: λ2x.t[x]
, 
top: Top
, 
satisfiable_int_formula: satisfiable_int_formula(fmla)
, 
decidable: Dec(P)
, 
ge: i ≥ j 
, 
assert: ↑b
, 
bnot: ¬bb
, 
guard: {T}
, 
sq_type: SQType(T)
, 
or: P ∨ Q
, 
exists: ∃x:A. B[x]
, 
bfalse: ff
, 
subtype_rel: A ⊆r B
, 
prop: ℙ
, 
not: ¬A
, 
false: False
, 
less_than': less_than'(a;b)
, 
le: A ≤ B
, 
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
, 
nat: ℕ
, 
uall: ∀[x:A]. B[x]
, 
member: t ∈ T
, 
init0: init0(a)
, 
baire_eq_from: baire_eq_from(a;k)
, 
implies: P 
⇒ Q
, 
all: ∀x:A. B[x]
Lemmas referenced : 
int_subtype_base, 
set_subtype_base, 
decidable__le, 
int_formula_prop_wf, 
int_formula_prop_le_lemma, 
int_formula_prop_less_lemma, 
int_term_value_constant_lemma, 
int_term_value_var_lemma, 
int_formula_prop_eq_lemma, 
int_formula_prop_not_lemma, 
int_formula_prop_and_lemma, 
intformle_wf, 
intformless_wf, 
itermConstant_wf, 
itermVar_wf, 
intformeq_wf, 
intformnot_wf, 
intformand_wf, 
satisfiable-full-omega-tt, 
decidable__equal_int, 
nat_properties, 
init0_wf, 
less_than_wf, 
assert-bnot, 
bool_subtype_base, 
subtype_base_sq, 
bool_cases_sqequal, 
eqff_to_assert, 
le_wf, 
nat_wf, 
equal_wf, 
and_wf, 
false_wf, 
assert_of_lt_int, 
eqtt_to_assert, 
bool_wf, 
lt_int_wf
Rules used in proof : 
computeAll, 
voidEquality, 
isect_memberEquality, 
intEquality, 
int_eqEquality, 
functionEquality, 
functionExtensionality, 
voidElimination, 
independent_functionElimination, 
cumulativity, 
instantiate, 
dependent_functionElimination, 
promote_hyp, 
dependent_pairFormation, 
because_Cache, 
lambdaEquality, 
applyEquality, 
applyLambdaEquality, 
dependent_set_memberEquality, 
levelHypothesis, 
addLevel, 
hyp_replacement, 
independent_pairFormation, 
independent_isectElimination, 
productElimination, 
equalitySymmetry, 
equalityTransitivity, 
equalityElimination, 
unionElimination, 
hypothesis, 
hypothesisEquality, 
rename, 
setElimination, 
natural_numberEquality, 
thin, 
isectElimination, 
sqequalHypSubstitution, 
extract_by_obid, 
introduction, 
cut, 
sqequalRule, 
lambdaFormation, 
sqequalReflexivity, 
computationStep, 
sqequalTransitivity, 
sqequalSubstitution
Latex:
\mforall{}a:\mBbbN{}  {}\mrightarrow{}  \mBbbN{}.  \mforall{}n:\mBbbN{}.    (init0(a)  {}\mRightarrow{}  init0(baire\_eq\_from(a;n)))
Date html generated:
2017_04_21-AM-11_24_40
Last ObjectModification:
2017_04_20-PM-06_48_53
Theory : continuity
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