Nuprl Lemma : separated-partitions_wf
∀I:Interval. ∀P,Q:partition(I). (separated-partitions(P;Q) ∈ ℙ) supposing icompact(I)
Proof
Definitions occuring in Statement :
separated-partitions: separated-partitions(P;Q),
partition: partition(I),
icompact: icompact(I),
interval: Interval,
uimplies: b supposing a,
prop: ℙ,
all: ∀x:A. B[x],
member: t ∈ T
Definitions unfolded in proof :
all: ∀x:A. B[x],
uimplies: b supposing a,
member: t ∈ T,
separated-partitions: separated-partitions(P;Q),
uall: ∀[x:A]. B[x],
partition: partition(I),
prop: ℙ
Lemmas referenced :
and_wf,
frs-increasing_wf,
frs-separated_wf,
partition_wf,
icompact_wf,
interval_wf
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
lambdaFormation,
isect_memberFormation,
introduction,
cut,
sqequalRule,
lemma_by_obid,
sqequalHypSubstitution,
isectElimination,
thin,
setElimination,
rename,
hypothesisEquality,
hypothesis,
independent_isectElimination,
lambdaEquality,
dependent_functionElimination,
axiomEquality,
equalityTransitivity,
equalitySymmetry,
because_Cache
Latex:
\mforall{}I:Interval. \mforall{}P,Q:partition(I). (separated-partitions(P;Q) \mmember{} \mBbbP{}) supposing icompact(I)
Date html generated:
2016_05_18-AM-09_27_55
Last ObjectModification:
2015_12_27-PM-11_20_41
Theory : reals
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