Nuprl Lemma : assert-nonneg-poly
∀[p:iPolynomial()]. uiff(↑nonneg-poly(p);(∀m∈p.↑nonneg-monomial(m)))
Proof
Definitions occuring in Statement :
nonneg-poly: nonneg-poly(p),
nonneg-monomial: nonneg-monomial(m),
iPolynomial: iPolynomial(),
l_all: (∀x∈L.P[x]),
assert: ↑b,
uiff: uiff(P;Q),
uall: ∀[x:A]. B[x]
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
nonneg-poly: nonneg-poly(p),
uiff: uiff(P;Q),
and: P ∧ Q,
uimplies: b supposing a,
l_all: (∀x∈L.P[x]),
all: ∀x:A. B[x],
iPolynomial: iPolynomial(),
int_seg: {i..j-},
lelt: i ≤ j < k,
le: A ≤ B,
less_than: a < b,
squash: ↓T,
decidable: Dec(P),
or: P ∨ Q,
not: ¬A,
implies: P ⇒ Q,
satisfiable_int_formula: satisfiable_int_formula(fmla),
exists: ∃x:A. B[x],
false: False,
top: Top,
prop: ℙ,
so_lambda: λ2x.t[x],
so_apply: x[s],
iff: P ⇐⇒ Q,
rev_implies: P ⇐ Q
Lemmas referenced :
assert_witness,
nonneg-monomial_wf,
select_wf,
iMonomial_wf,
int_seg_properties,
decidable__le,
full-omega-unsat,
intformand_wf,
intformnot_wf,
intformle_wf,
itermConstant_wf,
itermVar_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_var_lemma,
int_formula_prop_wf,
decidable__lt,
length_wf,
intformless_wf,
int_formula_prop_less_lemma,
l_all_wf,
assert_wf,
l_member_wf,
iff_weakening_uiff,
bl-all_wf,
assert-bl-all,
istype-assert,
nonneg-poly_wf,
iPolynomial_wf
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
Error :isect_memberFormation_alt,
introduction,
cut,
independent_pairFormation,
hypothesis,
sqequalRule,
sqequalHypSubstitution,
Error :lambdaEquality_alt,
dependent_functionElimination,
thin,
hypothesisEquality,
extract_by_obid,
isectElimination,
setElimination,
rename,
because_Cache,
independent_isectElimination,
productElimination,
imageElimination,
natural_numberEquality,
unionElimination,
approximateComputation,
independent_functionElimination,
Error :dependent_pairFormation_alt,
int_eqEquality,
Error :isect_memberEquality_alt,
voidElimination,
Error :universeIsType,
Error :functionIsTypeImplies,
Error :inhabitedIsType,
Error :setIsType,
promote_hyp,
independent_pairEquality,
Error :isectIsTypeImplies
Latex:
\mforall{}[p:iPolynomial()]. uiff(\muparrow{}nonneg-poly(p);(\mforall{}m\mmember{}p.\muparrow{}nonneg-monomial(m)))
Date html generated:
2019_06_20-PM-01_35_16
Last ObjectModification:
2019_04_08-PM-05_22_00
Theory : list_1
Home
Index