Nuprl Lemma : rpolydiv_wf
∀[n:ℤ]. ∀[a:ℕn + 1 ⟶ ℝ]. ∀[z:ℝ]. (rpolydiv(n;a;z) ∈ ℕn ⟶ ℝ)
Proof
Definitions occuring in Statement :
rpolydiv: rpolydiv(n;a;z),
real: ℝ,
int_seg: {i..j-},
uall: ∀[x:A]. B[x],
member: t ∈ T,
function: x:A ⟶ B[x],
add: n + m,
natural_number: $n,
int: ℤ
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
rpolydiv: rpolydiv(n;a;z),
nat: ℕ,
int_seg: {i..j-},
lelt: i ≤ j < k,
and: P ∧ Q,
all: ∀x:A. B[x],
decidable: Dec(P),
or: P ∨ Q,
uimplies: b supposing a,
not: ¬A,
implies: P ⇒ Q,
satisfiable_int_formula: satisfiable_int_formula(fmla),
exists: ∃x:A. B[x],
false: False,
top: Top,
prop: ℙ,
guard: {T}
Lemmas referenced :
primrec_wf,
real_wf,
subtract_wf,
int_seg_properties,
decidable__le,
full-omega-unsat,
intformand_wf,
intformnot_wf,
intformle_wf,
itermConstant_wf,
itermSubtract_wf,
itermVar_wf,
intformless_wf,
istype-int,
int_formula_prop_and_lemma,
istype-void,
int_formula_prop_not_lemma,
int_formula_prop_le_lemma,
int_term_value_constant_lemma,
int_term_value_subtract_lemma,
int_term_value_var_lemma,
int_formula_prop_less_lemma,
int_formula_prop_wf,
istype-le,
decidable__lt,
itermAdd_wf,
int_term_value_add_lemma,
istype-less_than,
radd_wf,
rmul_wf,
int_seg_wf
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation_alt,
introduction,
cut,
sqequalRule,
lambdaEquality_alt,
extract_by_obid,
sqequalHypSubstitution,
isectElimination,
thin,
hypothesis,
dependent_set_memberEquality_alt,
hypothesisEquality,
natural_numberEquality,
setElimination,
rename,
because_Cache,
productElimination,
dependent_functionElimination,
unionElimination,
independent_isectElimination,
approximateComputation,
independent_functionElimination,
dependent_pairFormation_alt,
int_eqEquality,
isect_memberEquality_alt,
voidElimination,
independent_pairFormation,
universeIsType,
applyEquality,
addEquality,
productIsType,
axiomEquality,
equalityTransitivity,
equalitySymmetry,
isectIsTypeImplies,
inhabitedIsType,
functionIsType
Latex:
\mforall{}[n:\mBbbZ{}]. \mforall{}[a:\mBbbN{}n + 1 {}\mrightarrow{} \mBbbR{}]. \mforall{}[z:\mBbbR{}]. (rpolydiv(n;a;z) \mmember{} \mBbbN{}n {}\mrightarrow{} \mBbbR{})
Date html generated:
2019_10_29-AM-10_15_11
Last ObjectModification:
2019_01_14-PM-07_12_50
Theory : reals
Home
Index