Nuprl Lemma : eq-upto-baire-eq-from
∀a:ℕ ⟶ ℕ. ∀p,n:ℕ. ((p ≤ n) ⇒ (a = baire_eq_from(a;n) ∈ (ℕp ⟶ ℕ)))
Proof
Definitions occuring in Statement :
baire_eq_from: baire_eq_from(a;k),
int_seg: {i..j-},
nat: ℕ,
le: A ≤ B,
all: ∀x:A. B[x],
implies: P ⇒ Q,
function: x:A ⟶ B[x],
natural_number: $n,
equal: s = t ∈ T
Definitions unfolded in proof :
decidable: Dec(P),
top: Top,
satisfiable_int_formula: satisfiable_int_formula(fmla),
lelt: i ≤ j < k,
ge: i ≥ j ,
assert: ↑b,
bnot: ¬bb,
guard: {T},
sq_type: SQType(T),
or: P ∨ Q,
exists: ∃x:A. B[x],
bfalse: ff,
prop: ℙ,
not: ¬A,
false: False,
less_than': less_than'(a;b),
le: A ≤ B,
subtype_rel: A ⊆r 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,
int_seg: {i..j-},
uall: ∀[x:A]. B[x],
member: t ∈ T,
baire_eq_from: baire_eq_from(a;k),
implies: P ⇒ Q,
all: ∀x:A. B[x]
Lemmas referenced :
int_seg_wf,
le_wf,
int_formula_prop_wf,
int_formula_prop_le_lemma,
int_term_value_var_lemma,
int_formula_prop_less_lemma,
int_formula_prop_not_lemma,
int_formula_prop_and_lemma,
intformle_wf,
itermVar_wf,
intformless_wf,
intformnot_wf,
intformand_wf,
satisfiable-full-omega-tt,
decidable__equal_int,
nat_properties,
int_seg_properties,
less_than_wf,
assert-bnot,
bool_subtype_base,
subtype_base_sq,
bool_cases_sqequal,
equal_wf,
eqff_to_assert,
false_wf,
int_seg_subtype_nat,
nat_wf,
assert_of_lt_int,
eqtt_to_assert,
bool_wf,
lt_int_wf
Rules used in proof :
functionEquality,
dependent_set_memberEquality,
computeAll,
voidEquality,
isect_memberEquality,
intEquality,
int_eqEquality,
lambdaEquality,
voidElimination,
independent_functionElimination,
cumulativity,
instantiate,
dependent_functionElimination,
promote_hyp,
dependent_pairFormation,
natural_numberEquality,
independent_pairFormation,
applyEquality,
independent_isectElimination,
productElimination,
equalitySymmetry,
equalityTransitivity,
equalityElimination,
unionElimination,
because_Cache,
hypothesis,
hypothesisEquality,
rename,
setElimination,
thin,
isectElimination,
sqequalHypSubstitution,
extract_by_obid,
introduction,
sqequalRule,
functionExtensionality,
cut,
lambdaFormation,
sqequalReflexivity,
computationStep,
sqequalTransitivity,
sqequalSubstitution
Latex:
\mforall{}a:\mBbbN{} {}\mrightarrow{} \mBbbN{}. \mforall{}p,n:\mBbbN{}. ((p \mleq{} n) {}\mRightarrow{} (a = baire\_eq\_from(a;n)))
Date html generated:
2017_04_21-AM-11_24_32
Last ObjectModification:
2017_04_20-PM-06_46_56
Theory : continuity
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