Nuprl Lemma : partitions_wf
∀[I:Interval]. ∀[p:ℝ List]. partitions(I;p) ∈ ℙ supposing icompact(I)
Proof
Definitions occuring in Statement :
partitions: partitions(I;p),
icompact: icompact(I),
interval: Interval,
real: ℝ,
list: T List,
uimplies: b supposing a,
uall: ∀[x:A]. B[x],
prop: ℙ,
member: t ∈ T
Definitions unfolded in proof :
icompact: icompact(I),
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,
all: ∀x:A. B[x],
not: ¬A,
false: False,
less_than': less_than'(a;b),
le: A ≤ B,
implies: P ⇒ Q,
and: P ∧ Q,
prop: ℙ,
partitions: partitions(I;p),
uimplies: b supposing a,
member: t ∈ T,
uall: ∀[x:A]. B[x]
Lemmas referenced :
interval_wf,
list_wf,
icompact_wf,
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
Rules used in proof :
equalitySymmetry,
equalityTransitivity,
axiomEquality,
hypothesis_subsumption,
promote_hyp,
productElimination,
imageElimination,
voidEquality,
voidElimination,
isect_memberEquality,
baseClosed,
unionElimination,
dependent_functionElimination,
lambdaFormation,
independent_pairFormation,
independent_isectElimination,
because_Cache,
natural_numberEquality,
functionEquality,
hypothesis,
hypothesisEquality,
thin,
isectElimination,
sqequalHypSubstitution,
extract_by_obid,
productEquality,
sqequalRule,
cut,
introduction,
isect_memberFormation,
sqequalReflexivity,
computationStep,
sqequalTransitivity,
sqequalSubstitution
Latex:
\mforall{}[I:Interval]. \mforall{}[p:\mBbbR{} List]. partitions(I;p) \mmember{} \mBbbP{} supposing icompact(I)
Date html generated:
2018_05_22-PM-02_06_02
Last ObjectModification:
2018_05_21-AM-00_18_27
Theory : reals
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