Nuprl Lemma : minus-poly_wf
∀[p:iPolynomial()]. (minus-poly(p) ∈ iPolynomial())
Proof
Definitions occuring in Statement :
minus-poly: minus-poly(p),
iPolynomial: iPolynomial(),
uall: ∀[x:A]. B[x],
member: t ∈ T
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
iPolynomial: iPolynomial(),
minus-poly: minus-poly(p),
all: ∀x:A. B[x],
int_seg: {i..j-},
so_lambda: λ2x.t[x],
uimplies: b supposing a,
sq_stable: SqStable(P),
implies: P ⇒ Q,
lelt: i ≤ j < k,
and: P ∧ Q,
squash: ↓T,
guard: {T},
so_apply: x[s],
prop: ℙ,
top: Top,
subtype_rel: A ⊆r B,
exists: ∃x:A. B[x],
nat: ℕ,
le: A ≤ B,
less_than: a < b,
subtract: n - m,
sq_type: SQType(T),
iMonomial: iMonomial(),
int_nzero: ℤ-o,
minus-monomial: minus-monomial(m),
imonomial-less: imonomial-less(m1;m2),
pi2: snd(t),
imonomial-le: imonomial-le(m1;m2)
Lemmas referenced :
map_wf,
iMonomial_wf,
minus-monomial_wf,
int_seg_wf,
length_wf,
all_wf,
imonomial-less_wf,
select_wf,
sq_stable__le,
less_than_transitivity2,
le_weakening2,
iPolynomial_wf,
subtype_rel_list,
top_wf,
non_neg_length,
map_length,
length_wf_nat,
nat_wf,
set_subtype_base,
le_wf,
int_subtype_base,
equal_wf,
lelt_wf,
subtract_wf,
minus-one-mul,
add-swap,
add-commutes,
add-associates,
add-mul-special,
two-mul,
mul-distributes-right,
zero-mul,
zero-add,
one-mul,
subtype_base_sq,
map-length,
and_wf,
less_than_wf,
select-map,
int_seg_properties,
nat_properties,
int_nzero_properties,
not_wf,
equal-wf-base,
sorted_wf,
subtype_rel_self,
list_subtype_base,
list_wf,
assert_wf,
intlex_wf
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation,
introduction,
cut,
sqequalHypSubstitution,
setElimination,
thin,
rename,
dependent_set_memberEquality,
extract_by_obid,
isectElimination,
hypothesis,
lambdaEquality,
hypothesisEquality,
lambdaFormation,
natural_numberEquality,
sqequalRule,
because_Cache,
independent_isectElimination,
independent_functionElimination,
productElimination,
imageMemberEquality,
baseClosed,
imageElimination,
dependent_functionElimination,
axiomEquality,
equalityTransitivity,
equalitySymmetry,
isect_memberEquality,
voidElimination,
voidEquality,
applyEquality,
independent_pairFormation,
dependent_pairFormation,
sqequalIntensionalEquality,
intEquality,
promote_hyp,
addEquality,
multiplyEquality,
instantiate,
cumulativity,
addLevel,
hyp_replacement,
applyLambdaEquality,
levelHypothesis,
productEquality
Latex:
\mforall{}[p:iPolynomial()]. (minus-poly(p) \mmember{} iPolynomial())
Date html generated:
2017_04_14-AM-08_58_40
Last ObjectModification:
2017_02_27-PM-03_41_19
Theory : omega
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