Nuprl Lemma : arctan-poly_wf
∀[x:ℝ]. ∀[k:ℕ]. (arctan-poly(x;k) ∈ ℝ)
Proof
Definitions occuring in Statement :
arctan-poly: arctan-poly(x;k),
real: ℝ,
nat: ℕ,
uall: ∀[x:A]. B[x],
member: t ∈ T
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
arctan-poly: arctan-poly(x;k),
nat: ℕ,
so_lambda: λ2x.t[x],
int_nzero: ℤ-o,
int_seg: {i..j-},
nequal: a ≠ b ∈ T ,
guard: {T},
ge: i ≥ j ,
lelt: i ≤ j < k,
and: P ∧ Q,
not: ¬A,
implies: P ⇒ Q,
uimplies: b supposing a,
satisfiable_int_formula: satisfiable_int_formula(fmla),
exists: ∃x:A. B[x],
false: False,
all: ∀x:A. B[x],
top: Top,
prop: ℙ,
subtype_rel: A ⊆r B,
true: True,
sq_type: SQType(T),
bool: 𝔹,
unit: Unit,
it: ⋅,
btrue: tt,
ifthenelse: if b then t else f fi ,
uiff: uiff(P;Q),
decidable: Dec(P),
or: P ∨ Q,
bfalse: ff,
bnot: ¬bb,
assert: ↑b,
so_apply: x[s]
Lemmas referenced :
rsum_wf,
int-rdiv_wf,
int_seg_properties,
nat_properties,
full-omega-unsat,
intformeq_wf,
itermAdd_wf,
itermMultiply_wf,
itermConstant_wf,
itermVar_wf,
int_formula_prop_eq_lemma,
int_term_value_add_lemma,
int_term_value_mul_lemma,
int_term_value_constant_lemma,
int_term_value_var_lemma,
int_formula_prop_wf,
equal-wf-base,
int_subtype_base,
nequal_wf,
eq_int_wf,
subtype_base_sq,
true_wf,
bool_wf,
eqtt_to_assert,
assert_of_eq_int,
rnexp_wf,
decidable__le,
intformand_wf,
intformnot_wf,
intformle_wf,
int_formula_prop_and_lemma,
int_formula_prop_not_lemma,
int_formula_prop_le_lemma,
le_wf,
eqff_to_assert,
equal_wf,
bool_cases_sqequal,
bool_subtype_base,
assert-bnot,
neg_assert_of_eq_int,
rminus_wf,
int_seg_wf,
nat_wf,
real_wf
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation,
introduction,
cut,
sqequalRule,
extract_by_obid,
sqequalHypSubstitution,
isectElimination,
thin,
natural_numberEquality,
setElimination,
rename,
because_Cache,
hypothesis,
lambdaEquality,
dependent_set_memberEquality,
addEquality,
multiplyEquality,
hypothesisEquality,
productElimination,
lambdaFormation,
independent_isectElimination,
approximateComputation,
independent_functionElimination,
dependent_pairFormation,
int_eqEquality,
intEquality,
dependent_functionElimination,
isect_memberEquality,
voidElimination,
voidEquality,
baseApply,
closedConclusion,
baseClosed,
applyEquality,
remainderEquality,
addLevel,
instantiate,
cumulativity,
equalityTransitivity,
equalitySymmetry,
unionElimination,
equalityElimination,
independent_pairFormation,
promote_hyp,
axiomEquality
Latex:
\mforall{}[x:\mBbbR{}]. \mforall{}[k:\mBbbN{}]. (arctan-poly(x;k) \mmember{} \mBbbR{})
Date html generated:
2018_05_22-PM-03_04_29
Last ObjectModification:
2017_10_23-PM-00_54_43
Theory : reals_2
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