Nuprl Lemma : increasing-baire-eq-from
∀a:ℕ ⟶ ℕ. ∀k:ℕ. (increasing-sequence(a) ⇒ increasing-sequence(baire_eq_from(a;k)))
Proof
Definitions occuring in Statement :
baire_eq_from: baire_eq_from(a;k),
increasing-sequence: increasing-sequence(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],
subtype_rel: A ⊆r B,
decidable: Dec(P),
top: Top,
satisfiable_int_formula: satisfiable_int_formula(fmla),
ge: i ≥ j ,
not: ¬A,
false: False,
assert: ↑b,
bnot: ¬bb,
guard: {T},
sq_type: SQType(T),
or: P ∨ Q,
prop: ℙ,
exists: ∃x:A. B[x],
bfalse: ff,
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,
baire_eq_from: baire_eq_from(a;k),
increasing-sequence: increasing-sequence(a),
implies: P ⇒ Q,
all: ∀x:A. B[x]
Lemmas referenced :
int_subtype_base,
set_subtype_base,
decidable__equal_int,
increasing-sequence_wf,
int_formula_prop_le_lemma,
intformle_wf,
decidable__le,
int_formula_prop_eq_lemma,
intformeq_wf,
le_wf,
nat_wf,
decidable__equal_nat,
int_formula_prop_wf,
int_formula_prop_not_lemma,
int_term_value_constant_lemma,
int_term_value_var_lemma,
int_term_value_add_lemma,
int_formula_prop_less_lemma,
int_formula_prop_and_lemma,
intformnot_wf,
itermConstant_wf,
itermVar_wf,
itermAdd_wf,
intformless_wf,
intformand_wf,
satisfiable-full-omega-tt,
nat_properties,
less_than_wf,
assert-bnot,
bool_subtype_base,
subtype_base_sq,
bool_cases_sqequal,
equal_wf,
eqff_to_assert,
assert_of_lt_int,
eqtt_to_assert,
bool_wf,
lt_int_wf
Rules used in proof :
functionEquality,
applyLambdaEquality,
dependent_set_memberEquality,
functionExtensionality,
applyEquality,
inlFormation,
computeAll,
independent_pairFormation,
voidEquality,
isect_memberEquality,
intEquality,
int_eqEquality,
lambdaEquality,
voidElimination,
independent_functionElimination,
cumulativity,
instantiate,
dependent_functionElimination,
promote_hyp,
dependent_pairFormation,
because_Cache,
independent_isectElimination,
productElimination,
equalitySymmetry,
equalityTransitivity,
equalityElimination,
unionElimination,
natural_numberEquality,
hypothesis,
hypothesisEquality,
rename,
setElimination,
addEquality,
thin,
isectElimination,
sqequalHypSubstitution,
extract_by_obid,
introduction,
cut,
sqequalRule,
lambdaFormation,
sqequalReflexivity,
computationStep,
sqequalTransitivity,
sqequalSubstitution
Latex:
\mforall{}a:\mBbbN{} {}\mrightarrow{} \mBbbN{}. \mforall{}k:\mBbbN{}. (increasing-sequence(a) {}\mRightarrow{} increasing-sequence(baire\_eq\_from(a;k)))
Date html generated:
2017_04_21-AM-11_24_27
Last ObjectModification:
2017_04_20-PM-06_44_58
Theory : continuity
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