Nuprl Lemma : poly-nth-deriv_wf
∀[n,d:ℕ]. ∀[a:ℕn + d ⟶ ℝ]. (poly-nth-deriv(n;a) ∈ ℕd ⟶ ℝ)
Proof
Definitions occuring in Statement :
poly-nth-deriv: poly-nth-deriv(n;a),
real: ℝ,
int_seg: {i..j-},
nat: ℕ,
uall: ∀[x:A]. B[x],
member: t ∈ T,
function: x:A ⟶ B[x],
add: n + m,
natural_number: $n
Definitions unfolded in proof :
poly-nth-deriv: poly-nth-deriv(n;a),
uall: ∀[x:A]. B[x],
member: t ∈ T,
nat: ℕ,
implies: P ⇒ Q,
false: False,
ge: i ≥ j ,
uimplies: b supposing a,
satisfiable_int_formula: satisfiable_int_formula(fmla),
exists: ∃x:A. B[x],
not: ¬A,
all: ∀x:A. B[x],
top: Top,
and: P ∧ Q,
prop: ℙ,
sq_type: SQType(T),
guard: {T},
decidable: Dec(P),
or: P ∨ Q,
bool: 𝔹,
unit: Unit,
it: ⋅,
btrue: tt,
ifthenelse: if b then t else f fi ,
uiff: uiff(P;Q),
subtype_rel: A ⊆r B,
bfalse: ff,
bnot: ¬bb,
assert: ↑b,
nequal: a ≠ b ∈ T ,
subtract: n - m
Lemmas referenced :
nat_properties,
satisfiable-full-omega-tt,
intformand_wf,
intformle_wf,
itermConstant_wf,
itermVar_wf,
intformless_wf,
int_formula_prop_and_lemma,
int_formula_prop_le_lemma,
int_term_value_constant_lemma,
int_term_value_var_lemma,
int_formula_prop_less_lemma,
int_formula_prop_wf,
ge_wf,
less_than_wf,
int_seg_wf,
real_wf,
nat_wf,
primrec0_lemma,
subtype_base_sq,
int_subtype_base,
zero-add,
decidable__le,
subtract_wf,
intformnot_wf,
itermSubtract_wf,
int_formula_prop_not_lemma,
int_term_value_subtract_lemma,
primrec-unroll,
eq_int_wf,
bool_wf,
eqtt_to_assert,
assert_of_eq_int,
less_than_transitivity1,
le_weakening,
less_than_irreflexivity,
eqff_to_assert,
equal_wf,
bool_cases_sqequal,
bool_subtype_base,
assert-bnot,
neg_assert_of_eq_int,
poly-deriv_wf,
itermAdd_wf,
int_term_value_add_lemma,
le_wf,
add-commutes,
add-associates,
add-swap
Rules used in proof :
sqequalSubstitution,
sqequalRule,
sqequalReflexivity,
sqequalTransitivity,
computationStep,
isect_memberFormation,
introduction,
cut,
extract_by_obid,
sqequalHypSubstitution,
isectElimination,
thin,
hypothesisEquality,
hypothesis,
setElimination,
rename,
intWeakElimination,
lambdaFormation,
natural_numberEquality,
independent_isectElimination,
dependent_pairFormation,
lambdaEquality,
int_eqEquality,
intEquality,
dependent_functionElimination,
isect_memberEquality,
voidElimination,
voidEquality,
independent_pairFormation,
computeAll,
independent_functionElimination,
axiomEquality,
equalityTransitivity,
equalitySymmetry,
functionEquality,
addEquality,
instantiate,
cumulativity,
because_Cache,
unionElimination,
equalityElimination,
productElimination,
applyEquality,
promote_hyp,
dependent_set_memberEquality
Latex:
\mforall{}[n,d:\mBbbN{}]. \mforall{}[a:\mBbbN{}n + d {}\mrightarrow{} \mBbbR{}]. (poly-nth-deriv(n;a) \mmember{} \mBbbN{}d {}\mrightarrow{} \mBbbR{})
Date html generated:
2017_10_03-PM-00_14_05
Last ObjectModification:
2017_07_28-AM-08_36_51
Theory : reals
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