Nuprl Lemma : hd-rev-pcs-mon-vars
∀X:polynomial-constraints(). (0 < ||rev(pcs-mon-vars(X))|| ∧ (hd(rev(pcs-mon-vars(X))) = [] ∈ (ℤ List)))
Proof
Definitions occuring in Statement :
pcs-mon-vars: pcs-mon-vars(X),
polynomial-constraints: polynomial-constraints(),
hd: hd(l),
length: ||as||,
reverse: rev(as),
nil: [],
list: T List,
less_than: a < b,
all: ∀x:A. B[x],
and: P ∧ Q,
natural_number: $n,
int: ℤ,
equal: s = t ∈ T
Definitions unfolded in proof :
all: ∀x:A. B[x],
member: t ∈ T,
uall: ∀[x:A]. B[x],
so_lambda: λ2x.t[x],
implies: P ⇒ Q,
prop: ℙ,
and: P ∧ Q,
subtype_rel: A ⊆r B,
uimplies: b supposing a,
iPolynomial: iPolynomial(),
int_seg: {i..j-},
sq_stable: SqStable(P),
lelt: i ≤ j < k,
squash: ↓T,
guard: {T},
so_apply: x[s],
iMonomial: iMonomial(),
top: Top,
so_lambda: λ2x y.t[x; y],
so_apply: x[s1;s2],
or: P ∨ Q,
assert: ↑b,
ifthenelse: if b then t else f fi ,
btrue: tt,
less_than: a < b,
less_than': less_than'(a;b),
false: False,
cons: [a / b],
bfalse: ff,
not: ¬A,
cand: A c∧ B,
iff: P ⇐⇒ Q,
rev_implies: P ⇐ Q,
pi2: snd(t),
sq_type: SQType(T),
nat: ℕ,
le: A ≤ B,
decidable: Dec(P),
uiff: uiff(P;Q),
subtract: n - m,
true: True,
ge: i ≥ j ,
polynomial-mon-vars: polynomial-mon-vars(init;p),
colength: colength(L),
nil: [],
it: ⋅,
polynomial-constraints: polynomial-constraints(),
pcs-mon-vars: pcs-mon-vars(X),
last: last(L),
select: L[n],
length: ||as||,
list_ind: list_ind
Lemmas referenced :
polynomial-constraints_wf,
list_induction,
iPolynomial_wf,
all_wf,
list_wf,
less_than_wf,
length_wf,
equal-wf-base,
list_accum_wf,
top_wf,
subtype_rel_list,
subtype_rel_set,
iMonomial_wf,
int_seg_wf,
imonomial-less_wf,
select_wf,
sq_stable__le,
less_than_transitivity2,
le_weakening2,
subtype_rel_product,
int_nzero_wf,
sorted_wf,
subtype_rel_self,
polynomial-mon-vars_wf,
equal-wf-T-base,
last_wf,
list-cases,
null_nil_lemma,
length_of_nil_lemma,
product_subtype_list,
null_cons_lemma,
length_of_cons_lemma,
false_wf,
equal_wf,
list_accum_nil_lemma,
list_accum_cons_lemma,
list_subtype_base,
int_subtype_base,
member-polynomial-mon-vars,
l_exists_wf,
equal-wf-base-T,
l_member_wf,
subtype_base_sq,
last_member,
nil_member,
length_wf_nat,
nat_wf,
decidable__lt,
not-lt-2,
condition-implies-le,
minus-add,
minus-one-mul,
zero-add,
minus-one-mul-top,
add-commutes,
add_functionality_wrt_le,
add-associates,
add-zero,
le-add-cancel,
nil_wf,
squash_wf,
true_wf,
nat_properties,
less_than_transitivity1,
less_than_irreflexivity,
ge_wf,
colength_wf_list,
spread_cons_lemma,
le_antisymmetry_iff,
decidable__le,
not-le-2,
le_wf,
subtract_wf,
not-ge-2,
less-iff-le,
minus-minus,
add-swap,
set_subtype_base,
insert_wf,
list-deq_wf,
int-deq_wf,
iff_weakening_equal,
non_nil_length,
insert-not-nil,
last-insert,
ite_rw_false,
cons_wf,
length-reverse,
hd-reverse-is-last,
pcs-mon-vars_wf
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
lambdaFormation,
cut,
introduction,
extract_by_obid,
hypothesis,
thin,
sqequalHypSubstitution,
isectElimination,
sqequalRule,
lambdaEquality,
intEquality,
functionEquality,
natural_numberEquality,
because_Cache,
hypothesisEquality,
productEquality,
applyEquality,
independent_isectElimination,
setElimination,
rename,
independent_functionElimination,
productElimination,
imageMemberEquality,
baseClosed,
imageElimination,
dependent_functionElimination,
setEquality,
isect_memberEquality,
voidElimination,
voidEquality,
unionElimination,
promote_hyp,
hypothesis_subsumption,
equalityTransitivity,
equalitySymmetry,
independent_pairFormation,
baseApply,
closedConclusion,
inlFormation,
instantiate,
cumulativity,
addEquality,
minusEquality,
addLevel,
hyp_replacement,
universeEquality,
equalityUniverse,
levelHypothesis,
intWeakElimination,
axiomEquality,
applyLambdaEquality,
dependent_set_memberEquality
Latex:
\mforall{}X:polynomial-constraints(). (0 < ||rev(pcs-mon-vars(X))|| \mwedge{} (hd(rev(pcs-mon-vars(X))) = []))
Date html generated:
2017_04_14-AM-09_03_44
Last ObjectModification:
2017_02_27-PM-03_44_20
Theory : omega
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