Nuprl Lemma : full-partition_wf
∀[I:Interval]. ∀[p:partition(I)]. (full-partition(I;p) ∈ ℝ List) supposing icompact(I)
Proof
Definitions occuring in Statement :
full-partition: full-partition(I;p),
partition: partition(I),
icompact: icompact(I),
interval: Interval,
real: ℝ,
list: T List,
uimplies: b supposing a,
uall: ∀[x:A]. B[x],
member: t ∈ T
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
uimplies: b supposing a,
full-partition: full-partition(I;p),
partition: partition(I),
prop: ℙ,
icompact: icompact(I),
and: P ∧ Q
Lemmas referenced :
cons_wf,
real_wf,
left-endpoint_wf,
append_wf,
right-endpoint_wf,
nil_wf,
partition_wf,
icompact_wf,
interval_wf
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation,
introduction,
cut,
sqequalRule,
lemma_by_obid,
sqequalHypSubstitution,
isectElimination,
thin,
hypothesis,
hypothesisEquality,
independent_isectElimination,
because_Cache,
setElimination,
rename,
axiomEquality,
equalityTransitivity,
equalitySymmetry,
isect_memberEquality,
productElimination
Latex:
\mforall{}[I:Interval]. \mforall{}[p:partition(I)]. (full-partition(I;p) \mmember{} \mBbbR{} List) supposing icompact(I)
Date html generated:
2016_05_18-AM-08_55_49
Last ObjectModification:
2015_12_27-PM-11_38_18
Theory : reals
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