Nuprl Lemma : baire-diff-from_wf
∀[a:ℕ ⟶ ℕ]. ∀[k:ℕ]. (baire-diff-from(a;k) ∈ ℕ ⟶ ℕ)
Proof
Definitions occuring in Statement :
baire-diff-from: baire-diff-from(a;k),
nat: ℕ,
uall: ∀[x:A]. B[x],
member: t ∈ T,
function: x:A ⟶ B[x]
Definitions unfolded in proof :
assert: ↑b,
bnot: ¬bb,
sq_type: SQType(T),
bfalse: ff,
top: Top,
exists: ∃x:A. B[x],
satisfiable_int_formula: satisfiable_int_formula(fmla),
or: P ∨ Q,
decidable: Dec(P),
ge: i ≥ j ,
guard: {T},
prop: ℙ,
not: ¬A,
false: False,
less_than': less_than'(a;b),
le: A ≤ B,
subtype_rel: A ⊆r B,
uimplies: b supposing a,
and: P ∧ Q,
uiff: uiff(P;Q),
ifthenelse: if b then t else f fi ,
btrue: tt,
it: ⋅,
unit: Unit,
bool: 𝔹,
implies: P ⇒ Q,
all: ∀x:A. B[x],
nat: ℕ,
baire-diff-from: baire-diff-from(a;k),
member: t ∈ T,
uall: ∀[x:A]. B[x]
Lemmas referenced :
assert-bnot,
bool_subtype_base,
subtype_base_sq,
bool_cases_sqequal,
eqff_to_assert,
equal_wf,
int_formula_prop_wf,
int_formula_prop_eq_lemma,
int_term_value_add_lemma,
int_term_value_var_lemma,
int_term_value_constant_lemma,
int_formula_prop_le_lemma,
int_formula_prop_not_lemma,
int_formula_prop_and_lemma,
intformeq_wf,
itermAdd_wf,
itermVar_wf,
itermConstant_wf,
intformle_wf,
intformnot_wf,
intformand_wf,
satisfiable-full-omega-tt,
decidable__le,
nat_properties,
le_wf,
false_wf,
add_nat_wf,
nat-pred_wf,
nat_wf,
assert_of_le_int,
eqtt_to_assert,
bool_wf,
le_int_wf
Rules used in proof :
functionEquality,
axiomEquality,
cumulativity,
instantiate,
promote_hyp,
independent_functionElimination,
computeAll,
voidEquality,
voidElimination,
isect_memberEquality,
intEquality,
dependent_pairFormation,
dependent_functionElimination,
applyLambdaEquality,
equalitySymmetry,
equalityTransitivity,
independent_pairFormation,
natural_numberEquality,
addEquality,
dependent_set_memberEquality,
hypothesisEquality,
functionExtensionality,
applyEquality,
int_eqEquality,
independent_isectElimination,
productElimination,
equalityElimination,
unionElimination,
lambdaFormation,
hypothesis,
because_Cache,
rename,
setElimination,
thin,
isectElimination,
sqequalHypSubstitution,
extract_by_obid,
lambdaEquality,
sqequalRule,
cut,
introduction,
isect_memberFormation,
sqequalReflexivity,
computationStep,
sqequalTransitivity,
sqequalSubstitution
Latex:
\mforall{}[a:\mBbbN{} {}\mrightarrow{} \mBbbN{}]. \mforall{}[k:\mBbbN{}]. (baire-diff-from(a;k) \mmember{} \mBbbN{} {}\mrightarrow{} \mBbbN{})
Date html generated:
2017_04_21-AM-11_23_36
Last ObjectModification:
2017_04_20-PM-05_45_53
Theory : continuity
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