Nuprl Lemma : const-poly_wf
∀[n:ℤ-o]. (const-poly(n) ∈ iPolynomial())
Proof
Definitions occuring in Statement :
const-poly: const-poly(n),
iPolynomial: iPolynomial(),
int_nzero: ℤ-o,
uall: ∀[x:A]. B[x],
member: t ∈ T
Definitions unfolded in proof :
iPolynomial: iPolynomial(),
uall: ∀[x:A]. B[x],
member: t ∈ T,
const-poly: const-poly(n),
iMonomial: iMonomial(),
all: ∀x:A. B[x],
top: Top,
int_seg: {i..j-},
so_lambda: λ2x.t[x],
uimplies: b supposing a,
int_nzero: ℤ-o,
sq_stable: SqStable(P),
implies: P ⇒ Q,
lelt: i ≤ j < k,
and: P ∧ Q,
squash: ↓T,
guard: {T},
so_apply: x[s],
prop: ℙ,
le: A ≤ B,
nequal: a ≠ b ∈ T ,
uiff: uiff(P;Q),
subtype_rel: A ⊆r B,
not: ¬A,
less_than': less_than'(a;b),
true: True,
false: False,
or: P ∨ Q,
subtract: n - m,
nat_plus: ℕ+,
less_than: a < b,
sorted: sorted(L),
exists: ∃x:A. B[x]
Lemmas referenced :
cons_wf,
length_of_cons_lemma,
length_of_nil_lemma,
int_seg_wf,
length_wf,
int_nzero_wf,
list_wf,
nil_wf,
all_wf,
imonomial-less_wf,
select_wf,
sq_stable__le,
less_than_transitivity2,
iMonomial_wf,
le_weakening2,
zero-add,
not-equal-implies-less,
not-equal-2,
less-iff-le,
add_functionality_wrt_le,
add-associates,
add-zero,
add-swap,
le-add-cancel2,
subtract_wf,
le_reflexive,
minus-one-mul,
one-mul,
add-mul-special,
two-mul,
add-commutes,
mul-distributes-right,
zero-mul,
false_wf,
omega-shadow,
less_than_wf,
mul-distributes,
mul-associates,
mul-commutes,
int_seg_properties,
int_nzero_properties,
sorted_wf,
subtype_rel_self,
less_than_transitivity1,
less_than_irreflexivity,
equal_wf,
minus-zero
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation,
introduction,
cut,
sqequalRule,
dependent_set_memberEquality,
extract_by_obid,
sqequalHypSubstitution,
isectElimination,
thin,
because_Cache,
independent_pairEquality,
hypothesisEquality,
hypothesis,
lambdaFormation,
dependent_functionElimination,
isect_memberEquality,
voidElimination,
voidEquality,
natural_numberEquality,
setElimination,
rename,
productEquality,
lambdaEquality,
independent_isectElimination,
independent_functionElimination,
productElimination,
imageMemberEquality,
baseClosed,
imageElimination,
axiomEquality,
equalityTransitivity,
equalitySymmetry,
addEquality,
intEquality,
applyEquality,
unionElimination,
multiplyEquality,
minusEquality,
independent_pairFormation,
dependent_pairFormation,
promote_hyp
Latex:
\mforall{}[n:\mBbbZ{}\msupminus{}\msupzero{}]. (const-poly(n) \mmember{} iPolynomial())
Date html generated:
2017_04_14-AM-08_59_38
Last ObjectModification:
2017_02_27-PM-03_42_00
Theory : omega
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