Nuprl Lemma : eq-upto-baire-diff-from
∀[a:ℕ ⟶ ℕ]. ∀[n:ℕ]. (a = baire-diff-from(a;n) ∈ (ℕn ⟶ ℕ))
Proof
Definitions occuring in Statement :
baire-diff-from: baire-diff-from(a;k),
int_seg: {i..j-},
nat: ℕ,
uall: ∀[x:A]. B[x],
function: x:A ⟶ B[x],
natural_number: $n,
equal: s = t ∈ T
Definitions unfolded in proof :
less_than': less_than'(a;b),
le: A ≤ B,
assert: ↑b,
bnot: ¬bb,
sq_type: SQType(T),
bfalse: ff,
or: P ∨ Q,
decidable: Dec(P),
subtype_rel: A ⊆r B,
prop: ℙ,
top: Top,
not: ¬A,
false: False,
exists: ∃x:A. B[x],
satisfiable_int_formula: satisfiable_int_formula(fmla),
lelt: i ≤ j < k,
ge: i ≥ j ,
guard: {T},
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],
int_seg: {i..j-},
nat: ℕ,
baire-diff-from: baire-diff-from(a;k),
member: t ∈ T,
uall: ∀[x:A]. B[x]
Lemmas referenced :
int_seg_wf,
false_wf,
int_seg_subtype_nat,
assert-bnot,
bool_subtype_base,
subtype_base_sq,
bool_cases_sqequal,
equal_wf,
eqff_to_assert,
le_wf,
nat-pred_wf,
int_formula_prop_wf,
int_formula_prop_less_lemma,
int_term_value_var_lemma,
int_formula_prop_le_lemma,
int_formula_prop_and_lemma,
intformless_wf,
itermVar_wf,
intformle_wf,
intformand_wf,
satisfiable-full-omega-tt,
nat_wf,
decidable__equal_int,
nat_properties,
int_seg_properties,
assert_of_le_int,
eqtt_to_assert,
bool_wf,
le_int_wf
Rules used in proof :
functionEquality,
axiomEquality,
independent_functionElimination,
cumulativity,
instantiate,
promote_hyp,
dependent_set_memberEquality,
addEquality,
computeAll,
independent_pairFormation,
voidEquality,
voidElimination,
isect_memberEquality,
intEquality,
int_eqEquality,
lambdaEquality,
dependent_pairFormation,
applyEquality,
dependent_functionElimination,
natural_numberEquality,
because_Cache,
independent_isectElimination,
productElimination,
equalitySymmetry,
equalityTransitivity,
equalityElimination,
unionElimination,
lambdaFormation,
hypothesis,
hypothesisEquality,
rename,
setElimination,
thin,
isectElimination,
sqequalHypSubstitution,
extract_by_obid,
sqequalRule,
functionExtensionality,
cut,
introduction,
isect_memberFormation,
sqequalReflexivity,
computationStep,
sqequalTransitivity,
sqequalSubstitution
Latex:
\mforall{}[a:\mBbbN{} {}\mrightarrow{} \mBbbN{}]. \mforall{}[n:\mBbbN{}]. (a = baire-diff-from(a;n))
Date html generated:
2017_04_21-AM-11_23_43
Last ObjectModification:
2017_04_20-PM-05_47_19
Theory : continuity
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