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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