Nuprl Lemma : poly-deriv_wf
∀n:ℕ. ∀a:ℕn + 1 ⟶ ℝ. (poly-deriv(a) ∈ ℕn ⟶ ℝ)
Proof
Definitions occuring in Statement :
poly-deriv: poly-deriv(a),
real: ℝ,
int_seg: {i..j-},
nat: ℕ,
all: ∀x:A. B[x],
member: t ∈ T,
function: x:A ⟶ B[x],
add: n + m,
natural_number: $n
Definitions unfolded in proof :
less_than: a < b,
le: A ≤ B,
prop: ℙ,
subtract: n - m,
top: Top,
not: ¬A,
implies: P ⇒ Q,
false: False,
exists: ∃x:A. B[x],
satisfiable_int_formula: satisfiable_int_formula(fmla),
or: P ∨ Q,
decidable: Dec(P),
ge: i ≥ j ,
lelt: i ≤ j < k,
uimplies: b supposing a,
and: P ∧ Q,
uiff: uiff(P;Q),
nat: ℕ,
int_seg: {i..j-},
uall: ∀[x:A]. B[x],
poly-deriv: poly-deriv(a),
member: t ∈ T,
all: ∀x:A. B[x]
Lemmas referenced :
rmul_wf,
int-to-real_wf,
add-member-int_seg2,
nat_properties,
decidable__le,
subtract_wf,
satisfiable-full-omega-tt,
intformand_wf,
intformnot_wf,
intformle_wf,
itermSubtract_wf,
itermConstant_wf,
itermVar_wf,
int_formula_prop_and_lemma,
int_formula_prop_not_lemma,
int_formula_prop_le_lemma,
int_term_value_subtract_lemma,
int_term_value_constant_lemma,
int_term_value_var_lemma,
int_formula_prop_wf,
add-subtract-cancel,
decidable__lt,
intformless_wf,
int_formula_prop_less_lemma,
lelt_wf,
int_seg_wf,
real_wf,
nat_wf
Rules used in proof :
functionEquality,
computeAll,
voidEquality,
voidElimination,
isect_memberEquality,
intEquality,
int_eqEquality,
dependent_pairFormation,
unionElimination,
dependent_functionElimination,
independent_pairFormation,
dependent_set_memberEquality,
independent_isectElimination,
productElimination,
because_Cache,
applyEquality,
natural_numberEquality,
hypothesis,
hypothesisEquality,
rename,
setElimination,
addEquality,
thin,
isectElimination,
sqequalHypSubstitution,
lemma_by_obid,
lambdaEquality,
sqequalRule,
cut,
lambdaFormation,
sqequalReflexivity,
computationStep,
sqequalTransitivity,
sqequalSubstitution
Latex:
\mforall{}n:\mBbbN{}. \mforall{}a:\mBbbN{}n + 1 {}\mrightarrow{} \mBbbR{}. (poly-deriv(a) \mmember{} \mBbbN{}n {}\mrightarrow{} \mBbbR{})
Date html generated:
2016_05_18-AM-10_08_05
Last ObjectModification:
2016_01_17-AM-00_37_44
Theory : reals
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