Nuprl Lemma : i-approx-compact
∀I:Interval. ∀n:ℕ+. ∀r:ℝ. ((r ∈ i-approx(I;n)) ⇒ icompact(i-approx(I;n)))
Proof
Definitions occuring in Statement :
icompact: icompact(I),
i-approx: i-approx(I;n),
i-member: r ∈ I,
interval: Interval,
real: ℝ,
nat_plus: ℕ+,
all: ∀x:A. B[x],
implies: P ⇒ Q
Definitions unfolded in proof :
all: ∀x:A. B[x],
implies: P ⇒ Q,
icompact: icompact(I),
and: P ∧ Q,
cand: A c∧ B,
member: t ∈ T,
prop: ℙ,
uall: ∀[x:A]. B[x],
i-nonvoid: i-nonvoid(I),
exists: ∃x:A. B[x]
Lemmas referenced :
i-approx-closed,
i-approx-finite,
i-member_wf,
i-approx_wf,
real_wf,
nat_plus_wf,
interval_wf
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
lambdaFormation,
independent_pairFormation,
cut,
lemma_by_obid,
sqequalHypSubstitution,
dependent_functionElimination,
thin,
hypothesisEquality,
hypothesis,
because_Cache,
isectElimination,
dependent_pairFormation
Latex:
\mforall{}I:Interval. \mforall{}n:\mBbbN{}\msupplus{}. \mforall{}r:\mBbbR{}. ((r \mmember{} i-approx(I;n)) {}\mRightarrow{} icompact(i-approx(I;n)))
Date html generated:
2016_05_18-AM-08_46_17
Last ObjectModification:
2015_12_27-PM-11_48_19
Theory : reals
Home
Index