Nuprl Lemma : iproper-length-iff
∀I:Interval. (i-finite(I) ⇒ (r0 < |I| ⇐⇒ iproper(I)))
Proof
Definitions occuring in Statement :
i-length: |I|,
iproper: iproper(I),
i-finite: i-finite(I),
interval: Interval,
rless: x < y,
int-to-real: r(n),
all: ∀x:A. B[x],
iff: P ⇐⇒ Q,
implies: P ⇒ Q,
natural_number: $n
Definitions unfolded in proof :
all: ∀x:A. B[x],
implies: P ⇒ Q,
iff: P ⇐⇒ Q,
and: P ∧ Q,
member: t ∈ T,
prop: ℙ,
uall: ∀[x:A]. B[x],
uimplies: b supposing a,
rev_implies: P ⇐ Q,
iproper: iproper(I),
i-length: |I|,
rsub: x - y,
cand: A c∧ B
Lemmas referenced :
rless_wf,
int-to-real_wf,
i-length_wf,
iproper_wf,
i-finite_wf,
interval_wf,
radd-preserves-rless,
rsub_wf,
right-endpoint_wf,
left-endpoint_wf,
radd_wf,
rminus_wf,
rless_functionality,
radd_comm,
radd_functionality,
req_weakening,
radd-rminus-assoc,
radd-zero-both,
iproper-length
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
lambdaFormation,
independent_pairFormation,
cut,
introduction,
extract_by_obid,
sqequalHypSubstitution,
isectElimination,
thin,
natural_numberEquality,
hypothesis,
hypothesisEquality,
independent_isectElimination,
dependent_functionElimination,
productElimination,
independent_functionElimination,
sqequalRule,
promote_hyp
Latex:
\mforall{}I:Interval. (i-finite(I) {}\mRightarrow{} (r0 < |I| \mLeftarrow{}{}\mRightarrow{} iproper(I)))
Date html generated:
2016_10_26-AM-09_28_50
Last ObjectModification:
2016_08_16-AM-10_58_03
Theory : reals
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