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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