Nuprl Lemma : sq_stable__partitions
∀I:Interval. ∀p:ℝ List. (icompact(I) ⇒ SqStable(partitions(I;p)))
Proof
Definitions occuring in Statement :
partitions: partitions(I;p),
icompact: icompact(I),
interval: Interval,
real: ℝ,
list: T List,
sq_stable: SqStable(P),
all: ∀x:A. B[x],
implies: P ⇒ Q
Definitions unfolded in proof :
icompact: icompact(I),
so_apply: x[s],
so_lambda: λ2x.t[x],
bfalse: ff,
cons: [a / b],
squash: ↓T,
less_than: a < b,
so_apply: x[s1;s2],
top: Top,
so_lambda: λ2x y.t[x; y],
it: ⋅,
nil: [],
select: L[n],
btrue: tt,
ifthenelse: if b then t else f fi ,
assert: ↑b,
or: P ∨ Q,
not: ¬A,
false: False,
less_than': less_than'(a;b),
le: A ≤ B,
uimplies: b supposing a,
and: P ∧ Q,
prop: ℙ,
member: t ∈ T,
uall: ∀[x:A]. B[x],
implies: P ⇒ Q,
all: ∀x:A. B[x],
partitions: partitions(I;p)
Lemmas referenced :
interval_wf,
list_wf,
icompact_wf,
sq_stable__rleq,
sq_stable__all,
sq_stable__frs-non-dec,
right-endpoint_wf,
length_of_cons_lemma,
null_cons_lemma,
product_subtype_list,
base_wf,
stuck-spread,
length_of_nil_lemma,
null_nil_lemma,
list-cases,
last_wf,
false_wf,
select_wf,
left-endpoint_wf,
rleq_wf,
real_wf,
length_wf,
less_than_wf,
frs-non-dec_wf,
sq_stable__and
Rules used in proof :
lambdaEquality,
independent_functionElimination,
hypothesis_subsumption,
promote_hyp,
productElimination,
imageElimination,
voidEquality,
voidElimination,
baseClosed,
unionElimination,
dependent_functionElimination,
independent_pairFormation,
because_Cache,
independent_isectElimination,
productEquality,
natural_numberEquality,
functionEquality,
isect_memberEquality,
hypothesis,
hypothesisEquality,
thin,
isectElimination,
sqequalHypSubstitution,
extract_by_obid,
introduction,
cut,
lambdaFormation,
computationStep,
sqequalTransitivity,
sqequalReflexivity,
sqequalRule,
sqequalSubstitution
Latex:
\mforall{}I:Interval. \mforall{}p:\mBbbR{} List. (icompact(I) {}\mRightarrow{} SqStable(partitions(I;p)))
Date html generated:
2018_05_22-PM-02_06_15
Last ObjectModification:
2018_05_21-AM-00_18_39
Theory : reals
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