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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