Nuprl Lemma : pcs-mon-vars_wf
∀[X:polynomial-constraints()]. (pcs-mon-vars(X) ∈ ℤ List List)
Proof
Definitions occuring in Statement :
pcs-mon-vars: pcs-mon-vars(X)
,
polynomial-constraints: polynomial-constraints()
,
list: T List
,
uall: ∀[x:A]. B[x]
,
member: t ∈ T
,
int: ℤ
Definitions unfolded in proof :
uall: ∀[x:A]. B[x]
,
member: t ∈ T
,
pcs-mon-vars: pcs-mon-vars(X)
,
polynomial-constraints: polynomial-constraints()
,
subtype_rel: A ⊆r B
,
uimplies: b supposing a
,
iPolynomial: iPolynomial()
,
so_lambda: λ2x.t[x]
,
int_seg: {i..j-}
,
sq_stable: SqStable(P)
,
implies: P
⇒ Q
,
lelt: i ≤ j < k
,
and: P ∧ Q
,
squash: ↓T
,
guard: {T}
,
all: ∀x:A. B[x]
,
so_apply: x[s]
,
iMonomial: iMonomial()
,
prop: ℙ
,
top: Top
,
so_lambda: λ2x y.t[x; y]
,
so_apply: x[s1;s2]
Lemmas referenced :
polynomial-constraints_wf,
polynomial-mon-vars_wf,
nil_wf,
cons_wf,
subtype_rel_self,
sorted_wf,
int_nzero_wf,
subtype_rel_product,
le_weakening2,
less_than_transitivity2,
sq_stable__le,
select_wf,
imonomial-less_wf,
length_wf,
int_seg_wf,
all_wf,
iMonomial_wf,
subtype_rel_set,
iPolynomial_wf,
subtype_rel_list,
top_wf,
list_wf,
list_accum_wf
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation,
introduction,
cut,
sqequalRule,
sqequalHypSubstitution,
productElimination,
thin,
lemma_by_obid,
isectElimination,
productEquality,
hypothesis,
intEquality,
because_Cache,
hypothesisEquality,
applyEquality,
independent_isectElimination,
lambdaEquality,
natural_numberEquality,
setElimination,
rename,
independent_functionElimination,
imageMemberEquality,
baseClosed,
imageElimination,
dependent_functionElimination,
setEquality,
isect_memberEquality,
voidElimination,
voidEquality,
lambdaFormation,
axiomEquality,
equalityTransitivity,
equalitySymmetry
Latex:
\mforall{}[X:polynomial-constraints()]. (pcs-mon-vars(X) \mmember{} \mBbbZ{} List List)
Date html generated:
2016_05_14-AM-07_10_11
Last ObjectModification:
2016_01_14-PM-08_41_01
Theory : omega
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